Given:
The total number of face cards is 12.
The total number of cards is 52.
The probability of 2 successive face cards is,
[tex]\begin{gathered} \frac{12\times11}{52\times51}=\frac{11}{13\times17} \\ =\frac{11}{221} \end{gathered}[/tex]The probability of not getting 2 face cards is,
[tex]\begin{gathered} P(\bar{E})=1-P(E) \\ =1-\frac{11}{221} \\ =\frac{210}{221} \end{gathered}[/tex]Next, to find the expected value.
[tex]\begin{gathered} \frac{11}{221}\times(-40)+\frac{210}{221}(10)=-\frac{440}{221}+\frac{2100}{221} \\ =\text{ \$}7.51 \end{gathered}[/tex]Hence, the expected value of the bet is $7.51.
