Question

a card is chosen from a standard deck of cards. what is the probability that the card is a queen, given that the card is a club?

Answer 1

Answer:

the correct answer was 1/13

Step-by-step explanation:

i took my test and put 4/13 which was wrong and said that 1/13 is the right answer

Answer 2

Answer:

Probability that card is queen given that card is club is $\frac{4}{13}$

Step-by-step explanation:

Given : A card is chosen from a standard deck of cards.

To find : What is the probability that the card is a queen, given that the card is a club?

Solution : It is the conditional probability

$P(A|B)=\frac{P(A\cap B)}{P(B)}$

Let A is probability that card is queen.

Let B is the probability that card is a club.

Probability that card is queen given card is club $P(A\cap B)=\frac{4}{52}=\frac{1}{13}$

Probability that card is club from deck of 52 cards $P(B)=\frac{13}{52}=\frac{1}{4}$

To find probability that card is queen given that card is club $P(A|B)$

$P(A|B)=\frac{P(A\cap B)}{P(B)}$

$P(A|B)=\frac{\frac{1}{13}}{\frac{1}{4}}$

$P(A|B)=\frac{1\times4}{13\times 1}=\frac{4}{13}$

Therefore, Option A is correct.

Probability that card is queen given that card is club is $\frac{4}{13}$