A card is picked at random from a pack of cards. Given that... | Mathematics | SolveeIt | Solveeit

Today, August 23

Question

A card is picked at random from a pack of cards. Given that the picked card is a Queen, what is the probability that it is a spade ?

A

$\frac{1}{3}$

B

$\frac{4}{13}$

C

$\frac{1}{4}$

D

$\frac{1}{2}$

Answer

$\frac{1}{4}$

Explanation

Solution

Let $A$ be the event that a card is queen and $B$ be the event that it is a spade.
Now, $P(B|A) = \frac{P(B\, \cap \,A)}{P(A)} = \frac{1 /52}{4/52} = \frac{1}{4}$