Question

Using a standard deck of playing cards, what is the probability of drawing a face card, replacing the card, and then drawing a seven? (Note: Face cards consist of kings, queens, and jacks in a deck.)

Answer 1

A typical deck has 12 face cards (4 kings, 4 queens, and 4 jacks) and 4 sevens. The odds of drawing and replacing a face card are 12/52, or 3/13. The odds of drawing a seven are 4/52 or 1/13.

We may multiply the probabilities to obtain the likelihood of both occurrences occurring:

(3/13) x (1/13) = 3/169

As a result, the chance of getting a face card, replacing it, and then drawing a seven is 3/169.