Question

a card is drawn from a standard deck of cards. find the probability, given that the card is black. p(club)
the probability that the card is a club given that the card is black is
(round to two decimal places as needed.)

Explanation:

Step1: Define conditional probability

Use formula $P(A|B)=\frac{P(A\cap B)}{P(B)}$, where $A$=club, $B$=black.

Step2: Find $P(A\cap B)$

A card is both club and black: there are 13 clubs. $P(A\cap B)=\frac{13}{52}=\frac{1}{4}$

Step3: Find $P(B)$

Black cards total 26. $P(B)=\frac{26}{52}=\frac{1}{2}$

Step4: Calculate conditional probability

Substitute values: $P(\text{club}|\text{black})=\frac{\frac{1}{4}}{\frac{1}{2}}=\frac{1}{4}\times2=\frac{1}{2}$

Step5: Convert to decimal

$\frac{1}{2}=0.50$

Answer:

0.50