What is the probability that the first card is an even card and the second card is Queen?

Question

Suppose you are going to draw two cards from a standard deck without replacement. What is the probability that the first card is an even card and the second card is Queen?

Answer 1

The probability of drawing an even card is the total number of even cards divided by the total number of cards. There are 5 even values (2,4,6,8,10) and 4 of each in the deck. That means there are 20 even cards in a deck of 52 cards. The probability is 20/52.

Next, the probability of drawing a Queen is calculated, but now there are only 51 cards total because you removed the first card. There are 4 Queens in a deck of 51 cards. The probability is 4/51.

Therefore, the probability of these two events is the product of the probability of each: (20/52)(4/51) = 20/663