Question

$4$ cards are drawn from the deck of $52$ cards. Find the probability of all $4$ cards drawn being Diamond if the cards are replaced.

• A. $\frac{1}{256}$
• B. $\frac{22}{4156}$
• C. $\frac{25}{4156}$
• D. $\frac{60}{4156}$

Answer 1

Answer: (A)

$\frac{1}{256}$

Given: $52$ cards, $4$ cards drawn with replacement.

To find: the probability of all 4 cards drawn being Diamond

According to the question

$n\left(S\right)=52$

Number of the diamond card in the pack is $13$

Hence the probability of all $4$ cards drawn being Diamond is

$=\frac{13}{52}\times \frac{13}{52}\times \frac{13}{52}\times \frac{13}{52}=\frac{1}{256}$