Question

Suppose you enter a contest where your probability of coming in first place is 0.37 and your probability of coming in second place is 0.33. If you come in first place, you win $56. If you come in second place, you win $36. If you don't come in first or second place, you have to pay $52. What is the expected value of this game?

Answer 1

It's expected to win $17 in this game

Explanation:

The expected value for a probability distribution is given by

`E(x)=\sum x_iP(x_i)`

In this problem, the set of x is

x={$56 , $36 , -$52}

Which have the respective set of probabilities:

p(x)={0.37 , 0.33 , 1-0.37-0.33 }={ 0.37 , 0.33 , 0.3 }

`E(x)=$56(0.37)+$36(0.33)-$52(0.3)=$17`

It's expected to win $17 in this game