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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