Question
Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let $$X$$ denote the random variable of number of aces obtained in the two drawn cards. Then $$P\left( {X = 1} \right) + P\left( {X = 2} \right)$$ equals:
A.
$$\frac{{49}}{{169}}$$
B.
$$\frac{{52}}{{169}}$$
C.
$$\frac{{24}}{{169}}$$
D.
$$\frac{{25}}{{169}}$$
Answer :
$$\frac{{25}}{{169}}$$
Solution :
$$X$$ = number of aces drawn
$$\eqalign{
& \therefore \,\,P\left( {X = 1} \right) + P\left( {X = 2} \right) \cr
& = \left\{ {\frac{4}{{52}} \times \frac{{48}}{{52}} + \frac{{48}}{{52}} \times \frac{4}{{52}}} \right\} + \left\{ {\frac{4}{{52}} \times \frac{4}{{52}}} \right\} \cr
& = \frac{{24}}{{169}} + \frac{1}{{169}} \cr
& = \frac{{25}}{{169}} \cr} $$