MDM4U Unit 2: Probability Distributions Test

MDM4U Unit 2: Probability Distributions Practice Questions

1. You are playing a game with your friends. The probability that you will win the game is 60%.

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?

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?

e) If you play the game 20 times, how many times do you expect to win, on average?

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.

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]

5. You are playing the following game:

- 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.

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.

Communication

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.

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:

(1/2) 3 (1/2) 6

Explain what is wrong with this solution and describe what the real solution should be.

 Thinking / Inquiry / 6

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]

2. You are playing a game with the following rules:

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.

What is the expected value of playing this game? [3]