Question

There are 52 playing cards in a standard deck of cards. If Patrica selects a card at random, what is the probability that it will be a black queen then a red card without replacing the first card.

Answer 1

Since there are two black queens out of 52 cards, there is a 2/52 chance of drawing a black queen first.  This is equivalent to a 1/26 chance.

Now that we have removed a black queen, there are 51 cards left in the deck.  26 of them are red because we only took away a black card.  This means that there is a 26/51 of drawing a red card next.

In order to find the probability of both of these happening, we multiply the two together.  1/26 * 26/51 = 26/1326.  This reduces to 1/51.  So, there is a 1/51 chance of drawing a black queen, then a red card.