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:
[tex]\begin{gathered} P(A)=\frac{Number\text{ of favorable outcome}}{total\text{ outcome }} \\ =\frac{4}{6} \end{gathered}[/tex]Amount is:
[tex]\begin{gathered} =3\times\frac{4}{6} \\ =\frac{12}{6} \end{gathered}[/tex]Probability for lose is:
Number of favorable outcome is:2
Total outcome is:6
so probability is:
[tex]P=\frac{2}{6}[/tex]So amount is:
[tex]\begin{gathered} A=1\times\frac{2}{6} \\ =\frac{2}{6} \end{gathered}[/tex]so total amount is:
win-lose amount :
[tex]\begin{gathered} \text{Expected value =}\frac{\text{12}}{6}-\frac{2}{6} \\ =\frac{12-2}{6} \\ =\frac{10}{6} \end{gathered}[/tex]