<p> MDM4U Unit 2: Probability Distributions Practice Questions</p><p>1. You are playing a game with your friends. The probability that you will win the game is 60%. </p><p> a) What is the probability that you will win 5 times in a row? b) What is the probability that you will lose two times in a row and then win the third time?</p><p> c) What is the probability that you will win two times out of three? d) On average, how long do you expect to play before you lose 1 game?</p><p> e) If you play the game 20 times, how many times do you expect to win, on average?</p><p>2. You want to estimate the number of students that will attend next year’s semi-formal dance. The school has 1200 students, and 4 out of the 20 that you polled said they want to go to the dance.</p><p> a) How many students do you expect will attend the dance? [1] b) Give at least two reasons why your solution in part a) might not be accurate [2]</p><p>5. You are playing the following game:</p><p>- You draw a card from a deck of 52 cards. If the card is red, you win $20 dollars. Determine the fair price of this game. </p><p>6. Create a probability distribution for the sum of rolling 2 tetrahedron die (4-sided). Note: this means you will need to draw a graph.</p><p>Communication</p><p>1. You are randomly sampling 20 people from Canada. You know that 10% of the population is left handed. Is this an example of a binomial probability distribution, or a hypergeometric probability distribution? Explain why.</p><p>2. Mr. Garrison wants to find the probability of flipping heads 3 times out of 9 when he flips a fair coin. He argues that the probability should be:</p><p>(1/2) 3 (1/2) 6</p><p>Explain what is wrong with this solution and describe what the real solution should be. </p><p> Thinking / Inquiry / 6</p><p>1. You are playing a best of 7 series of games with a friend (the first person to win 4 games is declared the winner and the series ends). In each individual game, you have a 70% chance of winning. What is the probability that you will win the series in exactly 7 games? [3]</p><p>2. You are playing a game with the following rules:</p><p>You are rolling 3 six sided dice at the same time. If you get triples (three of the same number) you win $10 dollars. If you get doubles (exactly two of the same number), you win $5 dollars.</p><p>What is the expected value of playing this game? [3]</p>