Each time you draw one card from the deck, there is a 13/52 = 1/4 probability of drawing a heart. If
is a random variable representing the number of hearts you draw, then

That is, the number of hearts you draw follows a binomial distribution across
trials and with success probability
.
You earn $4 for each heart that gets drawn; let
be the random variable denoting your total winnings. Then
.
Now,
![E[W]=4E[H]=4np=5](https://img.qammunity.org/2020/formulas/mathematics/high-school/wi9c2of3m0qrpfa35s7oxbpyy82zj8iem8.png)
and
![\mathrm{Var}[W]=16\mathrm{Var}[H]=16np(1-p)=15](https://img.qammunity.org/2020/formulas/mathematics/high-school/a3p18egz7zrzmiv29diojhdob7ckn24mk5.png)