Question

A person drawn a card from a pack of $52$ cards, replaces it & shuffles the pack. He continues doing this till the draws a spade. The probability that he will fail exactly the first two times is

• A. $\frac{1}{64}$
• B. $\frac{9}{64}$
• C. $\frac{36}{64}$
• D. $\frac{60}{64}$

Answer 1

Answer: (C)

$\frac{36}{64}$

Solution :-

Persons draws card till spade comes

probability of getting a spade = $\frac{1}{4}$

probability of not getting a spade = $1-\frac{1}{4}=\frac{3}{4}$

probability failing first two times = $\frac{3}{4}\times \frac{3}{4}=\frac{9}{16}=\frac{36}{64}$

C is correct.