Unit 2 Test Review KEY Name ______________________________

Part A Turbo gets “Traditional Plan” of $5 a week for allowance. He also loves to play basketball. Turbo wants to

convince his people to try something new with his allowance based on his basket-shooting talent, hoping that it will

increase what he receives. Turbo suggests the “Turbo makes a Bonus Basket Allowance Plan” instead of getting $5, he

will attempt shooting baskets each week for his allowance.

• If he misses the first basket, he gets only $3.

• If he makes (succeeds with) the first basket, he gets $10 and a chance to make another basket for an additional $5.

• Turbo can make a basket 55% of the time.

a. Make a model to describe this situation and the probabilities associated with each

possible outcome.

b. Over a one year period what is the expected sum of the “Traditional Plan” of the

$5 per week plan?

c. Over a one year period what is the total expected allowance of the “Turbo makes a

Bonus Basket Allowance Plan”?

Part B This Venn diagram represents social media use of all 100 students in three AMDM classes.

_______ 1. How many students use Both Facebook and Twitter?

_______ 2. How many students use Twitter?

________ 3. What is the probability that a student uses Facebook?

________ 4. What is the probability that a student does not use

Facebook or Twitter?

Part C Baseball has been very good to me. Organizers have set up game booths for the contestants. Turbo wants

to win a small stuffed animal. Use the chart to the right to find the

probability of a certain number of hits. The rules of the game are as

follows:

Turbo is pitched 3 fastballs, and he must hit them into a fair zone

to count.

If Turbo successfully hits all 3 pitches, he wins a small stuffed

animal that costs $5.

If Turbo successfully hits 2 pitches, he wins a pennant that costs $2.00.

If Turbo successfully hits 1 pitch, he wins a calculator that costs $1.00.

If Turbo misses all the pitches, he does not win a prize.

The game costs $3 to play (each set of 3 fastballs).

a. What is the expected payoff for a player of the game?

b. If 200 people were to play the game what is the expected loss or profit for the organizers?

c. If 200 people were to play the game and the small stuffed animal costs $10 and all of the other conditions

were the same what would be the expected loss or profit?

Part D At Turbo Farms, the corn maze has the paths shown.

Only some paths have a prize at the end of the path. These

winning paths are marked with a Y.

1. If only forward motion is allowed (no backtracking), draw

the area model for the corn maze.

2. What is the theoretical probability of winning a prize?

3. If 400 people go through the maze on a particular weekend, how many prizes should Turbo Farms expect to give away

that weekend?

4. Turbo charges $3 for entry into the maze. A prize is worth $8. What is Turbo’s profit or loss if 400 people go through

the maze?

Part E This area diagram represents the probability that Turbo will catch a chip monk during a hunt.

Y N N N

N Y

N N Y

N N

1. What is the overall probability that Turbo would catch a chip monk?

2. If Turbo were to go on 50 hunts how many chip monks would we expect him to catch?

Part F Turbo has applied to the University of Alabama,

the University of Georgia, and the University of Florida.

He thinks the probability that all three will admit him is

0.10. The probability that only Florida will admit him is

0.20. The probability that only Alabama will admit him

is 0.14. The probability that only Georgia will admit

him is 0.12. The probability that Georgia and Alabama

admit him while Florida denies him is 0.13. The

probability that Georgia and Florida admit him while

Alabama denies him is 0.05. The probability that

Alabama and Florida admit him while Georgia denies

him is 0.18.

(a) Complete a Venn diagram with all of the probabilities for Turbo’s college admission scenario.

(b) What is the probability that none of the schools admit Turbo?

(c) What is the probability that Florida admits him?

(d) What is the probability that both Alabama and Georgia admit him?