Question

From a pack of $52$ cards, two cards are drawn at random one after the other with replacement. What is the probability that both cards are kings?

• A. $\frac{1}{169}$
• B. $\frac{2}{169}$
• C. $\frac{5}{169}$
• D. None of these

Answer 1

Answer: (A)

$\frac{1}{169}$

Total number of cards $52$.

Given, two cards are drawn at random one after the other with replacement.

Total number of kings is $4$.

The probability of getting kings in the first draw is $\frac{4}{52}$.

The card is replaced.

Now the probability of getting kings in the second draw is $\frac{4}{52}$.

Thus the probability that both cards are kings is $\frac{4}{52}\times \frac{4}{52}=\frac{1}{169}$.