From a deck of 52 playing cards, two cards are drawn, one after the other without replacement. What is the probability that the first will be a king and the second will be a jack of the same suit?

Question

From a deck of 52 playing cards, two cards are drawn, one after the other without replacement. What is the probability that the first will be a king and the second will be a jack of the same suit? ​

Quizplus · Accepted Answer

There are 4 kings and 4 jacks in a deck of playing cards. Since the question specifies that the jack must be of the same suit as the king drawn, there are only 1 jack of the same suit remaining after drawing a king. Therefore, the probability of drawing a king as the first card is 4/52 (or 1/13) and the probability of drawing the matching jack as the second card is 1/51 (since there is one less card in the deck). The probabilities of these two events happening together is the product of their individual probabilities, which is (4/52) * (1/51) = 1/663.

From a Deck of 52 Playing Cards, Two Cards Are