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:

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

Amount is:

$\begin{gathered} =3\times\frac{4}{6} \\ =\frac{12}{6} \end{gathered}$

Probability for lose is:

Number of favorable outcome is:2

Total outcome is:6

so probability is:

$P=\frac{2}{6}$

So amount is:

$\begin{gathered} A=1\times\frac{2}{6} \\ =\frac{2}{6} \end{gathered}$

so total amount is:

win-lose amount :

$\begin{gathered} \text{Expected value =}\frac{\text{12}}{6}-\frac{2}{6} \\ =\frac{12-2}{6} \\ =\frac{10}{6} \end{gathered}$