# Assessment: random variables and expected value

1. Two \$20 bills, three \$10 bills, four \$5 bills, and six \$1 bills are placed in a bag. If a bill is chosen at random, what is the expected value for the amount chosen?

2. In a game you flip a coin twice and record the number of heads that occur. You get 20 points for 2 heads, 5 points for 1 head, and 5 points for no heads. What is the expected value for the number of points you’ll win per turn?

3. Consider a box with gift cards inside. The gift cards amounts are as follows: 10 gift cards with the amount of \$5 each, 7 gift cards with \$10 each, and 5 gift cards with \$25 each. Find the expected value for drawing a gift card from the box.

4. “ Wheel of Fortune” just got a new wheel! On it, there are 12 slots worth \$200, 8 slots worth \$400, 5 slots worth \$600, 6 slots with no money, 1 slot with \$5000, and 1 slot with a car worth \$25000.

a. What are the expected winnings on one turn (cash and prizes)?

b. If you get 12 spins, what are your expected winnings?

5. In a game, you roll a die. If you get a 1, you would win \$50. If you roll a 2or 4, you win \$30, and if you roll a 3, 5, or 6 you lose \$25. What is the expected value of one roll of the die?

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