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 $50, 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)

Complete the following probability distribution

x

P(x)

-$10

$10

$50

$100

(b) What is your expected winning or loss in this game? Be specific in the answer as to whether it's winning or loss.

x

P(x)

-$10

$10

$50

$100

Explanation / Answer

a) Here we are given the number of prizes for each prize value. That is divided by 100 ( that is the total number of spaces) to get the required probability. The probability density is computed as:

b) The expected winning in the game is computed as:

E(X) = -10*0.7 + 10*0.2 + 50*0.09 + 100*0.01

E(X) = -7 + 2 + 4.5 + 1 = 0.5

Therefore the expected winning in the game is 0.5

X P(X=x) -10 70/100 = 0.7 10 20/100 = 0.2 50 9/100 = 0.09 100 1/100 = 0.01

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