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 ?

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)  (1/3) (B)  (4/13) (C)  (1/4) (D)  (1/2)

Tardigrade Admin · Accepted Answer

Let A be the event that a card is queen and B be the event that it is a spade. Now, P(B|A) = (P(B ∩ A)/P(A)) = (1 /52/4/52) = (1/4)

Q. 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 ?

$\frac{1}{3}$

$\frac{4}{13}$

$\frac{1}{4}$

$\frac{1}{2}$

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