Suppose you are going to draw two cards from a standard deck. What is the probability that the first card is a Jack and the second card is an even card?

Answer 1

The probability of two independent events both happening is the probability of one happening times the probability of the second one happening.

The probability of event #1 (drawing a Jack) is 4/52 = 1/13 (because there are 4 jacks and 52 cards)

Since the even cards are 2, 4, 6, 8, and 10, there are 5 cards in each of the 4 suits so 20 cards. The probability of event #2 happening (assuming you did not replace the first draw) is 20/51.

So the probability of both events happening is 1/13•20/51 = 20/663 or about 3%