Conditional Card Probability

P(B|A) with playing card examples

P(King | Picture Card)

Question

You draw a card and are told it is a "picture card" (a card with a picture - Jack, Queen, or King). What is the probability that it is a King?

x 4 suits

Picture cards (also called face cards) are:

Given we drew a picture card, our sample space is:

J♠

J♥

J♦

J♣

Q♠

Q♥

Q♦

Q♣

K♠

K♥

K♦

K♣

Kings among picture cards:

Answer

This is the "classic" conditional probability example from the presets! Among picture cards, each rank (J, Q, K) is equally likely.

P = 1/3

Unconditional

About 7.7%

Conditional

About 33.3%

Knowing we have a picture card increases the probability of King from 7.7% to 33.3%!