Probability Distributions Final Assignment

Probability Distributions Final Assignment

Name: ______________________

Knowledge Application Thinking Communication

/ 13 / 14 Knowledge:

For the following situations (all using a standard deck of cards), determine whether it is Binomial (B), Geometric (G), Hypergeometric (H) or None (N) (2 K).

_____Choose 5 cards (with replacement). What is the probability that you get 3 Queens?

_____Choose a card. You win $5 if its a face card, $10 if its an ace and nothing otherwise.

_____Choose 5 cards (without replacement). What is the probability that you get 3 Queens?

_____Choose one card at a time (with replacement). What is the probability that you get the first Queen on the 10th try?

The probability of the Toronto Maple Leafs winning any basketball game is 32%.

Determine the probability of them finally winning their first game on their 7th game (2 K).

How many games should we expect the Leafs to lose before they have one win? (1 K)

Mr. K has to decide how many homework questions he will check at the end of the night. If the class works hard (with a probability of 15%) he will only check 3 questions. If they are somewhat lazy (probability of 20%) he will check 8 questions. The only other possibility is that they are very lazy and he will check 15 questions.

What is the expected number of questions that will be checked? (3 K)

The probability that you pass a unit test is 78%

Determine the probability distribution of passing unit tests, if there are 3 in total (4 K)

b) What is the expected number of tests you pass? (1 K)

Application:

A student has a part time job selling magazine subscriptions door-to-door. The following table shows the outcomes of a particular day.

Outcome Percent

The home owner closes the door in his face no sale 45

No one answered the door no sale 34

Someone answered the door and spoke to him, but no sale 16

Someone came to the door and he makes a sale 5

What is the probability of him making his first sale on the 8th attempt? (3 A)

At a swim meet there are a total of 22 competitors, and 10 of them belong to Clarkson swim team. 6 swimmers race at a time in heats.

a) In the heat of 6 swimmers, how many are expected to be from Clarkson? (2 A)

b) What is the probability that at least 2 of the swimmers are from Clarkson? (3 A)

Mr. K designed a simple board game, see diagram below. Each player places their token at the start, a single die is rolled to determine the number of steps to move. The game ends when a players token lands on Finish. When an odd number is rolled, player moves forward by the number rolled. When an even number is rolled, player moves backward by half the number rolled.

Start Finish

a) Show the probability distribution for the number of moves every time a die is rolled (3 A)

b) What is the expected number of times a player has to roll the die to finish the game? (3 A)

Thinking:

8. A student designs a casino game with the following outcomes ($5 per play):

Jackpot win your money back plus $50, probability of 10%

Win win your money back plus $10, probability of 20%

Tie win your money back, probability of 20%

Lose probability of 50%

This results in an expected value of $4.50. This means that each time the player plays, they will win an average of $4.50. She wants the game to be in her favour, but only slightly so the game appears fair.

Explain two different methods that she can use to get the desired result. For each method, show the change in the expected value mathematically to prove your point. Explanations will contribute to your communication mark.

Method #1:

Method #2: