Answer
$\$3.11$
Work Step by Step
John only wins $5$ dollars if both balls are white.
The probability of $2$ white balls:
$\dfrac{8}{10}\times \dfrac{7}{9} = \dfrac{56}{90}$.
The denominator and numerator both decrease by one because a white ball has been removed from the bag.
The expected value is:
$5\times \dfrac{56}{90}=\dfrac{280}{90}\approx 3.11$
John can expect to win $\$3.11$.
