Imagine you are in a game show. There are 20 prizes hidden on a game board with

Question

Imagine you are in a game show. There are 20 prizes hidden on a game board with 100 spaces. One prize is worth $50, nine are worth $20, and another ten are worth $10. You have to pay $5 to the host if your choice is not correct. Let the random variable x be the money you get or lose. Show all work. especially for (a).

(a) Complete the following probability distribution.

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

Explanation / Answer

As there are 100 spaces your probability of hitting any of the spaces is the same at 1/100.

1 out of 100 will get you 50.
3 out of 100 will get you 20.
6 out of 100 will get you 10.
the rest will get you nothing.

You put up 5 dollars so you're out 5 dollars to start with.

p(x) = -5 + 1/100 * 50 + 3/100 * 20 + 6/100 * 10

=> p(x) = -3.3

b)
Each ticket is expected to lose 3 dollars and 30 cents on the average.
That is -
the 50 dollar ticket will get you 45 dollars (50 - 5).
the 20 dollar tickets will get you 15 dollars (20 - 5).
the 10 dollar ticket will get you 5 dollars (10 - 5).
the rest of the tickets will get you -5 dollars (0 - 5).

p(x) = 1/100 * 45 + 3/100 * 15 + 6/100 * 5 + 90/100 * -5.
=> p(x) = -3.3
Thus, we are at loss.

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