Question

Noah and William play a game by rolling the die. If the die shows 1, 2, 4, or 5, then they will win $3. Otherwise, they will lose $1. Find the expected value. A) 1B) 9/6C) -10/6D) 10/6

Answer 1

Given:

die is 1,2,4,5 win amount is $3.

otherwise lose is $1.

Probability for win is:

Number of favorable outcome is =4

total out come is :6

so probability is:

`\begin{gathered} P(A)=\frac{Number\text{ of favorable outcome}}{total\text{ outcome }} \\ =(4)/(6) \end{gathered}`

Amount is:

`\begin{gathered} =3*(4)/(6) \\ =(12)/(6) \end{gathered}`

Probability for lose is:

Number of favorable outcome is:2

Total outcome is:6

so probability is:

`P=(2)/(6)`

So amount is:

`\begin{gathered} A=1*(2)/(6) \\ =(2)/(6) \end{gathered}`

so total amount is:

win-lose amount :

`\begin{gathered} \text{Expected value =}\frac{\text{12}}{6}-(2)/(6) \\ =(12-2)/(6) \\ =(10)/(6) \end{gathered}`