Question

In the carnival game "chuck-a-luck", you pick a number from 1 to 6 and roll 3 dice in succession. If your number comes up all three times, you win $3; if your number comes up twice, you win $2; if it comes up once, you win $1; otherwise you lose $1. What is your expected value

Answer 1

42 cents

Explanation:

Data provided in the question:

Random variable i.e gain with values 3,2,1,-1.

Now,

The corresponding probabilities will be as follows:

`P(3)=(\frac 16)^(3)`

`P(2)=3*(\frac 16)^(3)`

`P(1)=3*(\frac 16)^(3)`

`P(-1)=1-7(\frac 13)^(3)`

Expected gain =
`3*(\frac 16)^(3)+2*3*(\frac 16)^(3)+1*3*(\frac 16)^(3)-1*\left(1-7*(\frac 13)^(3)\right)`

Expected gain =
`(\frac 13)^(3)[3+6+3-(0.7407)]`

`=(\frac 16)^(3)[11.2593]=0.4170`

≈ 42 cents