Two cards drawn successively with replacement from 52 cards.

Question

Two cards drawn successively with replacement from 52 cards. $X$=number of aces. Find $P(X=1)+P(X=2)$.

Accepted Answer

$$P(X=1) = 2\times\frac{4}{52}\times\frac{48}{52}=\frac{24}{169},\qquad P(X=2)=\left(\frac{4}{52}\right)^2=\frac{1}{169}$$

$$P(X=1)+P(X=2) = \frac{25}{169}$$

Solutions · 1