Imagine you are in a game show. There are 30 prizes hidden on a game board with

Question

Imagine you are in a game show. There are 30 prizes hidden on a game board with 100 spaces. One prize is worth $100, nine are worth S50, and another twenty are worth $10. You have to pay $10 to the host if your choice is not correct. Let the random variable x be the money you get or lose. Show all work. Just the answer, without supporting work, will receive no credit. (a) Complete the following probability distribution. -$10 $10 $50 $100 b) What is your expected winning or loss in this game? Be specific in your answer whether it's winning or loss.

Explanation / Answer

(a) There is one $100 prize out of 100.

=> Probability of a square resulting into a $100 square = 1/100 = 0.01.

There are nine $50 prizes out of 100.

=> Probability of a square resulting into a $50 square = 9/100 = 0.09.

There are twenty $10 prizes out of 100.

=> Probability of a square resulting into a $10 square = 20/100 = 0.2.

70 squares have no prize

=> Probability of a square resulting into no prize = 70/100 = 0.7.

(b) Expected value E(x) = -$10 * 0.7 + $10 * 0.2 + $50 * 0.09 + $100 * 0.01

= 0.5$.

Since the expected value is positive, the expected winning is 0.5$.

x P(x) -$10 0.7 $10 0.2 $50 0.09 $100 0.01

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