If you have a 1/4 probability of gaining $500 and a 3/4 probability of losing $2

Question

If you have a 1/4 probability of gaining $500 and a 3/4 probability of losing $200, what is your expected value? If you have a 1/10 probability of gaining $200, a 3/10 probability of losing $300, and a 6/10 probability of breaking even, what is your expected value? A die is thrown. If an even number comes up, a person receives $10, otherwise the person loses $20. Find the expected value of the game. One hundred lottery tickets are sold for $2 each. one prize of $50 will be awarded. John purchases one ticket. Find his expectation. Ron rolls a die. If hr rolls a 3, Charles will give him $ 4. If Ron does not roll a 3, he must give Charles $1. Find Ron's expectations.

Explanation / Answer

a) Expected value = 1/4 * 500 - 3/4 * 200 = -25

b) Expected value = 1/10 * 200 - 3/10 * 300 + 6/10 * 0 = -70

c) P(even number) = 3/6 = 0.5

Expected value = 0.5 * 10 - 0.5 * 10 = 0

d) Expected value =1/100 * 50 - 99/100 * 2 = -1.48

e) P(3) = 1/6

Expected value = 1/6 * 4 - 5/6 * 1 = -0.167

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