Coin Probability Problems

From its physical properties, we assume the probability of heads is 0. Find out about the probabilitites of winning with each different type of bet in roulette, as well as the probabilities of other interesting roulette events. a journal of intriguing probability problems. the opposite face is either heads or tails, the desired probability is 1/2. In fact, the probability for most other values virtually disappeared — including the probability of the coin being fair (Bias = 0. a What is the probability that a red ball is drawn?. Therefore, the problem can be rewritten as !, which ends up being equal to 120. Probability, physics, and the coin toss L. Demonstrates frequency and probability distributions with weighted coin-flipping experiments Graphs solution curves for initial value problems with a first-order. Every flip of the coin has an “independent probability“, meaning that the probability that the coin will come up heads or tails is only affected by the toss of the coin itself. The formula:. coin toss probability calculator,monte carlo coin toss trials. Coin tossing probability - Sample space When a coin is tossed, there are two possible outcomes. The probability of rolling a six on the fifth roll is 1/6, the same as the probability of rolling a six on any given individual roll. An ideal unbiased coin might not correctly model a real coin, which could be biased slightly one way or another. What is the probability that there are exactly 2 Heads and 3 tails? Five men and three women applied for 2 scholarships. Probability. (1) What is the probability that all coins land heads? (2) What is the probability that all coins land heads if the first coin is heads? (3) What is the probability that all coins land heads if at least one coin lands heads? Read solution. When looking at the probability of the event that the coin lands on tail we get the following:. 7E-20 A fair coin is tossed 20 times. We toss a fair coin three times. It will guide you on how to understand a question and how to really proceed with finding the solution. Knowing probability and its applications are important to work effectively on data science problems and this post will remind you what actually is a probability. Intersection of Events, P(A∩B) - When two events are fulfilled simultaneously. In probability, we talk about events" and outcomes. Probability Problems in Game Design. ) (a)Make a table of the PDF of X. The sample space S for a probability model is the set of all possible outcomes. "Coin" Word Problems. Probabilit nth say and tha aange tee hing. Your function should use only foo(), no other library method. From Probability For Dummies. It can either be heads or tails. Byju's Coin Toss Probability Calculator is a tool which makes calculations very simple and interesting. This means that the probability of the coin landing on heads would be ½. 1) The mathematical theory of probability assumes that we have a well defined repeatable (in principle) experiment, which has as its outcome a set of well defined, mutually exclusive, events. For instance, a coin flip has two possible outcomes: heads or tails. Using Wolfram|Alpha's broad computational understanding of probability and expansive knowledge of real-world applications of probability theory, you can compute the chances of winning various games driven by random chance, conduct and analyze the experimental outcomes of random trials, visualize. This paper discusses the theory of Collective Intelligence (COIN) using the modified version of Probability Collectives (PC) to achieve the global goal. Experimental Probability. What is the probability that 3 heads occur before 8 tails? Unfortunately, this can be interpreted in two ways, and I neglected to ask which he intended. in the first three tosses of a fair/unbiased coin. But unfortunately you do not know the value of q, and it could be rational or irrational!. For example, suppose there are 5 marbles in a bowl. Check out the full article at the link below for probability charts and a fascinating look into the mathematics of solving coin toss probability problems. Two marbles are drawn with replacement. The final way we will chart these problems is the area model. Click Image to Enlarge : Toss enough coins to make a prediction about probability (maximum number of tosses 1000, but you can keep tossing to get a larger data set). For instance, you can calculate the probability that you'll win the lottery or be chosen in a group of people. When all outcomes of an event are equally likely, the probability that the event will happen is given by the ration below. Getting at least $2$ heads when flipping a coin $3$ times but the coin is biased so that heads are $3$ times more likely than tails. 3 to 5, what is the probability that she will win first prize? Problem 36. In the case of a coin toss, the probability that it will land with the "heads" side up is 50 percent. In fact, the probability for most other values virtually disappeared — including the probability of the coin being fair (Bias = 0. Even a half-dollar is still a whole-coin. Each time you toss these coins, there are four possible outcomes: both heads penny head & dime tail penny tail & dime head both tails You will flip the pair of coins 20 times. (This is called a Bernoulli random variable. Find the probability of obtaining a result of heads. Then the math behind the puzzles was explored. The interrupted game of chance (Fermat). Most of the high level science and math careers center around the mastery of these skills. A problem based on probability, 999 coins and one two-headed coin? There is a jar with 999 fair coins and one two-headed coin. The probability of getting Rs 20 coin is 1 f. Review: Fifty Challenging Problems in Probability with Solutions User Review - Robert - Goodreads. For instance, you can calculate the probability that you'll win the lottery or be chosen in a group of people. We can also see the probability that either A or B will happen. What is the probability that: (a) We get exactly one head. There will be total 20 MCQ in this test. Probability quantifies the likelihood of an event. If a red coin was moved from box A to box B, then box B has 7 red coins and 3 blue coins. Factorials are very useful in statistics and probability. What is the probability that the first coin you flip is the unfair coin? You have three identical-looking coins in front of you. PHY306 Homework 1. Find probability if you spin the spinner once for P (even number) Jill tossed a coin. For example, for the occupancy problem (Problems 3, 4 and 5), if the number of cells is higher than 6, it is quite easy and natural to scale up the transition probability matrix to include additional states. By looking at the events that can occur, probability gives us a framework for making predictions about how often events will happen. There are a large number of probability distributions available, but we only look at a few. When tossing a coin, the total possible outcomes are two, heads and tails. It's generally the total number of ways for the favorable or expected event or events to occur divided by the the total outcomes of the sample space S. On the other hand, the probability that you can swim around the world in 30 hours is nearly 0, as is the probability that you will win the lottery some day. The probability of 3 throws being tails is 1/2*1/2*1/2=1/8. Coin Toss Probability Calculator. Problem 730. Discussion/Introduction. How likely something is to happen. A biased coin is tossed 6 times. If you are, I'd like to know how to solve this particular problem (This is a pseudo coin-flip question) The probability of a new born baby is a boy is 50% and that of a new born baby is a girl is 50%. Interestingly some of these problems are classic problems in probability (tossing coins, rolling dice, occupancy problem, coupon collector problem). What is the probability of rolling a number less than 4 and tossing a coin that lands on tails? The outcome on the die does not affect the outcome of the coin. For example, if a coin is balanced well, there is no reason for it to land heads in preference to tails when it is tossed vigorously, so according to the Theory of Equally Likely Outcomes, the probability that the coin lands heads is equal to the probability that the coin lands tails, and both are 100%/2 = 50%. At most three times?Solution: Let F denote the event that the coin lands heads at most three times. Probability is the study of making predictions about random phenomena. (1) What is the probability that all coins land heads? (2) What is the probability that all coins land heads if the first coin is heads? (3) What is the probability that all coins land heads if at least one coin lands heads? Read solution. Two gamblers, A and B, are betting on the tosses of a fair coin. Problem 1 is a mathematical probability problem while problem 2 is a statistical one that can use the mathematical probability model determined in Problem 1 as a tool to seek a solution. A probability of 1. For example, suppose we have three coins. From the above problem. Example You can find the experimental probability of getting a head when you toss a coin by tossing a coin 20 times and keeping track of the outcomes. PHY306 Homework 1. At the beginning of the game, player A has 1 coin and player B has 3 coins. He was the author or co-author of more than 350 scholarly papers and more than 50 books, including one of the most popular books in his field, first published in 1965 and reprinted by Dover in 1987, Fifty Challenging Problems in Probability with Solutions. I TheSample Space Some sources and uses of randomness, and philosophical conundrums. Coin Problem. Starting with this definition, it would (probably :-) be right to conclude that the Probability Theory, being a branch of Mathematics, is an exact, deductive science that studies uncertain quantities related to random events. Probability is the study of making predictions about random phenomena. Coin Toss: Simulation of a coin toss allowing the user to input the number of flips. You toss three coins and get three heads. Do your math problems yourself and use it as a tool to check your answers! You can also enter word problems, but dont be too fancy. , 25%) or as a proportion between 0 and 1 (e. What is the probability of selecting a blue car with a 6-cylinder engine and an automatic transmission? Draw a tree diagram for questions 5 and 6. For example, the probability of the combination HTT is (1/2)(1/2)(1/2) = 1/8. The calculator generates solution with detailed explanation. The major challenge is to make these agents work in a coordinated way, optimizing their local utilities and contributing the maximum towards optimization of the global objective. The probability of rolling a head is ½ and the probability of rolling a tail is ½. Formula, lesson and practice problems explained step by step. Some probability questions Nikos Apostolakis 1 Coins 1. For the problems below, find the probability of each event described and the probability of its complement. If you are, I'd like to know how to solve this particular problem (This is a pseudo coin-flip question) The probability of a new born baby is a boy is 50% and that of a new born baby is a girl is 50%. Numerous people have tried to explain why they think the answer is 1/2, arguing that since both coins have a head then seeing a head doesn't rule out anything and thus it could be either coin with equal probability. Homework Students flip a coin. Consider the “experiment” of flipping a coin. In what follows, S is the sample space of the experiment in question and E is the event of interest. When the probability of an event is zero then the even is said to be impossible. The number of permutations of a set is the number of different ways in which the elements of the set can be arranged (or ordered). The probability of 3 throws being tails is 1/2*1/2*1/2=1/8. "At least two" is also "2 or more" , ">=2", "2,3,4,5, " "At most two" is also "two or less", "<=2", "0,1,2". Statistical models have a number of parameters that can be modified. Don't expect the numbers from trials to exactly match the predicted results--especially if you run only a few trials. Apparently, this means that heads-up appears more frequently. The advanced topics can be skipped if you are a new student of probability, or can be studied later, as the need arises. The probability that the coin will be 50p is 5/7 b. What is a fair price to pay for a single ticket in this raffle? Exercise 4. Because each coin toss is independent, we can multiply the probabilities together. For instance, you can calculate the probability that you'll win the lottery or be chosen in a group of people. Probability PLEPAVOUPAGLE OUTcomes. Example: Flipping a coin 10 times and landing on tails 7 times. Durham and Flournoy [5] proposed the biased coin design (BCD), which is an up-and-down design that assigns a new patient to a dose depending upon whether or not the current patient experienced a DLT. Actual GMAT Qunat problems deal with probability in a simpler, much more manageable way. Combinatorial problems, distributions, expectation, law of large numbers and central limit theorem, Bernoulli processes, and Markov chains. Learn more about the Chance and Probability problems and examples at vedantu. Tossing a Biased Coin Michael Mitzenmacher When we talk about a coin toss, we think of it as unbiased: with probability one-half it comes up heads, and with probability one-half it comes up tails. Two gamblers, A and B, are betting on the tosses of a fair coin. Apparently, this means that heads-up appears more frequently. According to the definition, probability is a function on the subsets of a sample space. intuitive probability and random processes using matlab. A Coin Toss Example An unbiased coin is tossed six times. Theoretical probability is the probability that is calculated using math formulas. Examples: In the experiment of flipping a coin, the mutually exclusive outcomes are the coin landing either heads up or tails up. hence leave the coins in the form of 11n always. Possible outcomes are head or tail. In this problem, we will use the R programming language to simulate. Can anyone explain how uneven probability works?. Problem: A bag contains (x) one rupee coins and (y) 50 paise coins. Coco the Parrot - Probability - Answer questions about the probability of simple and independent events. This is Article 1 in a series of stand-alone articles on basic probability. A coin is tossed once. There are a large number of probability distributions available, but we only look at a few. Find the expected value of det(A A0) as a function of n), where A0 is the transpose of A. The values represent the denominations of different coins, where these denominations have greatest common divisor of 1. (this problem is harder than what would be on the exam, but it is a useful application of probability for those interested in genetics) Each hereditary trait in an offspring depends on a pair of genes, one contributed by the father and the other by the mother. Please solve the following probability practice problems: Determine the probability that a digit chosen at random from the digits 1, 2, 3, …12 will be odd. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. This problem serves as a warmup for the more detailed calculations below. The complement rule is especially useful in the case where it hard to compute the probability of an event, but it is relatively easy to compute the probability of "not" the event. Some are simple exercises suitable for beginners, while others require more sophisticated techniques. The game has to end in a finite number of coin flips with probability 1. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%. In coin tossing example, the simple outcomes would be: heads or tails. Probability is a chance of prediction. Probability Questions with Solutions. However, not all dependent event problems are that simple. Type Acoins are fair, with probability 0. For example, the probability of getting at least one head when both coins are tossed in the air at the same time is: P(Head) = 3/4 = 0. Before starting anything just do a math practice set. ) What is the probability of getting heads on at least one flip? 3. A coin is randomly selected from the box and thrown into the air. The sum of probabilities of all sample points in a sample space is equal to 1. Then n(F) is given by the sum of the number of ways the coin lands heads zero, one, two, or three times. Tossing a Biased Coin Michael Mitzenmacher When we talk about a coin toss, we think of it as unbiased: with probability one-half it comes up heads, and with probability one-half it comes up tails. Simple experiment some well-defined act or process that leads to a single well-defined outcome. Because when you flip a coin you always have the probability of (1/2) or 50% and you never withdraw anything, like a marble. What are the chances of getting year six students to love learning about probability? They will be one hundred to one when you incorporate our year six probability worksheets. If you are beginner then this video will really help you in tackling problems related to coin experiment and it's probability in a better manner. Be sure to try the interactive probability activities, too!. Extension: Now you have a coin that shows heads with probability q, where 0 < q < 1. Call the probability of flipping heads p, and that of tails q. Note: Including the words "single time" and "after" confuse this problem somewhat. For example, suppose we wish to compute the probability of tossing at least one head in 10 tosses of a coin. (e) We get two heads. Probability Plaza: Probability by Surprise: Probability Games: Train Race: Math Goodies Probability: Fish Tank: Guessing Game : Dice Activities: Probability Games: Data Analysis & Probability Games: Coin Flipping Page: Coin Toss: What are Your Chances? What Are Your Chances? Probability Spinner: Spinner Adjustable Spinner: Marbles: Two Colors. With this view of probability, it makes perfectly good sense intuitively to talk about the probability that the Dow Jones average will go up tomorrow. So, after 500 flips most of the probability gets distributed around the value 0. Let there be integers with. The probability of heads on any toss is 0:3. The probability of an event is between 0 and 1. SEE MORE : 9. Coin toss probability formula along with problems on getting a head or a tail, solved examples on number of possible outcomes to get a head and a tail with probability formula @Byju's. Statistical Quality Control Multiple choices: 1. What if the dice aren't fair, or aren't independent of each other? Then each outcome {(a,b)} is assigned a probability (a number in [0,1]) whose sum over all 36 outcomes is equal to 1. Once we do that you can see that it is a simple combination problem. For instance, you can calculate the probability that you'll win the lottery or be chosen in a group of people. Some are simple exercises suitable for beginners, while others require more sophisticated techniques. When an official tosses a coin in the air at the beginning of a football game and one of the team captains calls “heads” or “tails,” what is the probability of the flipped coin coming up heads? Probability can be defined as “the likelihood that an event will occur. Probability problems for aptitude pdf download, probability problems and solutions for aptitude, probability problems, random variables and probability distributions problems and solutions, probability word problems with solutions and answers, probability distribution problems and solutions, probability problems on balls with solutions, basic. Recognize the binomial probability distribution and apply it appropriately. Came across an interesting problem today. This is for question a, so the probability for different outcomes for an unfair coin would not matter if it was a fair coin, the probability would be the same as a fair coin? This is for question b, fair or unfair coin, the # of outcome of heads would not matter? I am just a little comfused. Write all the elementary events in an experiment of tossing an unbiased coin. This video is a guide to probability. A discrete probability distribution is a table (or a formula) listing all possible values that a discrete variable can take on, together with the associated probabilities. Extension: Now you have a coin that shows heads with probability q, where 0 < q < 1. Probabilities are usually given as percentages. If the coin is flipped 50 times and it lands on heads 28 times, then the theoretical probability is 28/50. Download this year's Mathcounts handbook here. 00 means the event will always occur. Sets of data that record counts of actual, physical things are discrete. Blaise Pascal and Pierre de Fermat invented probability theory in 1654 to solve a gambling problem related to expected outcomes. When the probability of an event is zero then the even is said to be impossible. The other coin is biased with ℙ H = 2 3. Example= 17 coins now i picked 6 coins so 11 coins are there so u picked 10 coins then i will pick 1 coin and will be the winner. 3 to 5, what is the probability that she will win first prize? Problem 36. We'll use the TI 83 to do this now. Personal or subjective probability: These are values (between 0 and 1 or 0 and 100%) assigned by individuals based on how likely they think events are to occur. Stanford University conducted a study of coin flips. It is the ratio of the number of ways an event can occur to the number of possible outcomes. Solution: We know foo() returns 0 with 60% probability. This exercise illustrates the idea of different states that a system can take and gives a feel for the statistics involved. This kind of event forms the basis of your understanding of probability and enables you to find solutions to everyday problems that seem far removed from coin tossing or card drawing. 7870 and the probability of getting three or more heads in a row or three or more tails in a row is 0. Most questions answered within 4 hours. A coin is selected at random and tossed 5 times and all 5 results are heads. Regardless of the initial state, eventually the process will enter state 0 or state 4. From its physical properties, we assume the probability of heads is 0. Topics include: basic combinatorics, random variables, probability distributions, Bayesian inference, hypothesis testing, confidence intervals, and linear regression. Don't expect the numbers from trials to exactly match the predicted results--especially if you run only a few trials. When a coin is tossed, there is a chance of getting either a heads or a tails and hence the chances are 50% percentfor each. Example 4 If a coin is tossed twice, what is the probability that on the first toss the coin lands heads and on the second toss the coin lands tails? a) 1/6 b) 1/3 c) ¼ d) ½. 1 Probability, Conditional Probability and Bayes Formula The intuition of chance and probability develops at very early ages. Discrete Random Variables 4. So, yes, the observation matters. Problems in Elementary Probability Theory. The game has to end in a finite number of coin flips with probability 1. However, we don’t always live in a perfect world. What is the probability that it takes three flips or more for a coin to land heads up? What is the probability of a coin landing heads up 18 times in a row? What is the probability of getting at least one 6 in four throws of a single six-sided die? What is the probability of getting at least one double-six in 24 throws of two six-sided dice?. Four balls are placed in a bowl. Starting with this definition, it would (probably :-) be right to conclude that the Probability Theory, being a branch of Mathematics, is an exact, deductive science that studies uncertain quantities related to random events. For example, the probability of the combination HTT is (1/2)(1/2)(1/2) = 1/8. Define Success first. Theoretical probability is when you know what to expect because it has to be that way, like the probability of getting heads when you flip a coin is P( heads ) = 0. The probability can be any rational or irrational number between 0 and 1. Manually going through the combinatorics to determine the probability of an event occuring. So you might be wondering why I went off into permutations and combinations in the probability playlist, and I think you'll learn in this video. Buffon's Coin Experiment. Probability is the chance or likelihood that an event will happen. a journal of intriguing probability problems. Successfully working your way through probability problems means understanding some basic rules of probability along with discrete and continuous probability distributions. 5 and its similar for tossing the tails. Call the probability of flipping heads p, and that of tails q. Probability (Day 2) – Green Problems Find each event’s probability by showing all of the possible outcomes. If you are beginner then this video will really help you in tackling problems related to coin experiment and it's probability in a better manner. When we throw a coin on the air, the coin appears either a Head (H) or a Tail (T). In probability, we talk about events" and outcomes. Assume a fair coin in which the probability for ipping Head (H) is p(H) = 1=2 and the probability of ipping Tail (T) is p(T) = 1=2. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. b) Two coins are tossed, find the probability that one head only is obtained. When solving more complicated probability problems, we may need to consider series of random experiments or experiments that involve several different aspects, such as drawing two cards from a deck or rolling several dice. After having gone through the stuff given above, we hope that the students would have understood, "Probability Practice Problems Worksheet for Grade 10". We express probability as a number between 0 and 1. Important Facts. The term gambler's ruin is a statistical concept expressed in a variety of forms:. The types of probability problems shown here are simple events, like the odds of choosing something or winning something. A discrete probability distribution is a table (or a formula) listing all possible values that a discrete variable can take on, together with the associated probabilities. So, the probability of the coin landing on heads is 1/2. Basic Concepts. In the main program, all problems are. When two coins are tossed, probability of getting a Head (H) in the first toss and getting a Tail (T) in the second toss. This book is an update to the author's original coin toss book (The Coin Toss: Probabilities and Patterns), expanding on run distributions and statistics, as well as a new chapter containing 26 problems and solutions. PUTNAM PROBLEMS PROBABILITY AND STATISTICS 2016-B-4. Practice Problem 5-I For the Markov chain in Problem 5-E, determine the probability that the last toss involves only one coin. A fair coin is tossed 3 times. In the case of the coin flipping, the probability of the coin landing on tails is 1/2 or 0. Problem 16 Solution Yes, the answer is 2/3. This lesson is about coin based probability problems for upcoming bank exams. This is a distribution over the bias of a bernoulli process. probability of the coin landing heads up exactly six times? 4) A six-sided die is rolled six times. For example, suppose we have three coins. We've covered probability associated with One coin and two coins in this video. Events in Probability. A more complicated game with coins. If we want all of the ten outcomes to be head then what will be the probability for this? Solution: In one toss for head to come as outcome the probability is $\frac{1}{2}$. How to assess whether a coin tossed 900 times and comes up heads 490 times is biased? The probability. For each possible outcome of the first event, we draw a line where we write down the probability of that outcome and the state of the world if that outcome happened. The page count has increased by over 40 percent. Homework Students flip a coin. Be sure to try the interactive probability activities, too!. P (tails) = 7/10 P( heads) = 3/10. What is the probability that at least two babies are boys?. An outcome is the result of a single trial of an experiment. "Coin" Word Problems. 5 and its similar for tossing the tails. To check intuitive ideas like this, we shall flnd it helpful to look at some of these problems experimentally. In the problem above, the experiment is spinning the spinner. Given N number of coins, the task is to find probability of getting at least K number of heads after tossing all the N coins simultaneously. 7th Grade Math: Probability Problems. New videos every. Original question: What is the probability of getting only three heads with 10 coin flips? There are 2 possibilities for each coin flip and 10 flips so the total number of outcomes is $2^{10}=1024. "At least two" is also "2 or more" , ">=2", "2,3,4,5, " "At most two" is also "two or less", "<=2", "0,1,2". Some problems are easy, some are very hard, but each is interesting in some way. For example, if the chance of A happening is 50%, and the same for B, what are the chances of both happening, only one happening , at least one happening, or neither happening, and so on. There are two parameters, the number of times an experiment is done (n) and the probability of a success (p). Predict: How many times do you think the coins will both land on tails?. These course notes accompany Feller, An Introduction to Probability Theory and Its Applications, Wiley, 1950. It is taken from the document titled Nuances of Probability. It is the ratio of the number of ways an event can occur to the number of possible outcomes. It has six faces and each of the six faces shows a different number of dots from 1 to 6. 7870 and the probability of getting three or more heads in a row or three or more tails in a row is 0. Probability and statistics Here is a list of all of the skills that cover probability and statistics! These skills are organized by grade, and you can move your mouse over any skill name to preview the skill. The coins probably end up with the heavier side down more often than not. Other similar algebra word problems may involve items with specific values like stamps or tickets. Note: Probability is a funny thing. The probability of an event is between 0 and 1. A coin is tossed once. If events are independent, then the probability of them both occurring is the product of the probabilities of each occurring. If a coin is now taken at random from the bag, what is the probability that it is a one rupee coin? Answers: Case I: Let the first coin removed be one rupee coin One rupee coins left = (x – 1) Fifty paise coins left = y. The point is that the order of events doesn't affect with respect to conditional probability. These experiments are considered to be among the first problems in geometric probability. There are three boxes: a box containing two gold coins, a box containing two silver coins, a box containing one gold coin and one silver coin. EXAMPLE: What is the probability of not drawing a black marble from a box containing 6 white, 3 red, and 2 black marbles? SOLUTION: The probability of drawing a black marble from the box is. Probability of Tossing. One box contains three coins. What is the probability of the die coming up with a number greater than 3 ? 4. For instance, you can calculate the probability that you'll win the lottery or be chosen in a group of people. 5 for any given flip. This post discusses the problem of the gambler's ruin. By theory, we can calculate this probability by dividing number of expected outcomes by total number of outcomes. Types of Probability Sampling Simple Random Sampling. Exercise 13. On a mission to transform learning through computational thinking, Shodor is dedicated to the reform and improvement of mathematics and science education through student enrichment. laboratory for conducting simulation experiments to solve probability problems. John has a special die that has one side with a six, two sides with twos and three sides with ones. 4 Tree diagrams (EMBJW). 3 Sam is Coach more often. After all, real life is rarely fair. Example 1: A fair coin is tossed 5 times. The probability can be any rational or irrational number between 0 and 1. A fair coin is tossed 3 times. In probability theory, the probability is calculated for the favorable events to occur. Perform 5 sets of 10 coin flips, recording the results on your worksheet.