Question

if we draw a card from a standard deck, how to calculate this probability: p(drawing any king | the draw is a face card)?
1/52
4/52
4/12
4/13

Explanation:

Step1: Identify number of face - cards and kings

A standard deck has 52 cards. Face - cards are Jacks, Queens, and Kings. There are 3 types of face - cards and 4 suits, so there are $3\times4 = 12$ face - cards. There are 4 kings in a deck.

Step2: Calculate conditional probability

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the case of drawing a card, when $A$ is the event of drawing a king and $B$ is the event of drawing a face - card, $A\cap B$ is the event of drawing a king (since kings are face - cards). So $P(\text{drawing any king}|\text{the draw is a face card})=\frac{\text{Number of kings}}{\text{Number of face - cards}}=\frac{4}{12}$.

Answer:

C. 4/12