If two cards are randomly selected, what is the probability of drawing any one suit first, followed by drawing a face card

Question

If two cards are randomly selected, what is the probability of drawing any one suit first, followed by drawing a face card

in progress 0
1 year 2021-09-03T16:45:37+00:00 1 Answers 18 views 0

0.0181 = 1.81% probability of drawing a suit first, and then a face card.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Probability of drawing a suit first:

4 out of 52 cards are suits, so:

$$P(A) = \frac{4}{52} = \frac{1}{13}$$

Followed by drawing a face card:

Considering a suit was drawn, there will be 12 faces in the 51 remaining cards. So

$$P(B|A) = \frac{12}{51}$$

What is the probability of drawing a suit first, followed by drawing a face card?

$$P(A \cap B) = P(A) \times P(B|A) = \frac{1}{13} \times \frac{12}{51} = \frac{12}{13*51} = 0.0181$$

0.0181 = 1.81% probability of drawing a suit first, and then a face card.