Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that all the five cards are spades?

$(\frac{1}{4})^5$

The correct answer is Option (2) → $(\frac{1}{4})^5$

Let E be the event of 'drawing a card of spades', then

$p = P(E)=\frac{13}{52}=\frac{1}{4}$, so $q = 1-\frac{1}{4}=\frac{3}{4}$

As 5 cards are drawn with replacement, so there are 5 Bernoullian trials i.e. $n = 5$.

Thus, we have a binomial distribution with $p =\frac{1}{4},q=\frac{3}{4}$ and $n=5$.

Required probability = P(all five cards are spades) = P(5)

$={^5C}_5p^5=1.(\frac{1}{4})^5=(\frac{1}{4})^5$