Question

Two cards are drawn successively with replacement from a well-shuffled pack of $52$ cards. The probability of drawing two aces is.

• A. $\frac{1}{13}$
• B. $\frac{1}{13}\times \frac{1}{17}$
• C. $\frac{1}{52}\times \frac{1}{51}$
• D. $\frac{1}{13}\times \frac{1}{13}$

Answer 1

The correct option is D $\frac{1}{13}\times \frac{1}{13}$

Total cards $=52$

Two cards are drawn successively with replacement

$\Rightarrow$ One card is drawn and seen and then it is kept back.

$P[$drawing two aces$]=P[$drawing an ace$]\times P[$drawing an ace$]$

$=\frac{{}^4{C}_1}{{}^{52}{C}_1}\times \frac{{}^4{C}_1}{{}^{52}{C}_1}$

$=\frac{4}{52}\times \frac{4}{52}$

$=\frac{1}{13}\times \frac{1}{13}$