A card is drawn from a well-shuffled deck of 52 cards and then a second card is drawn. Find the probability that the first card is a heart and the second card is diamond if the first card is not replaced.

Question

Philoid · Accepted Answer

There are 52 cards in a deck. Let A be the event that first card drawn is a heart. There are 13 hearts in the pack. Hence, the probability of the first card is a heart is

Let B be the event that second card is a diamond without replacement. Then there are 13 diamond cards in the pack but as the cards are not replaced now there are 51 cards in total in the deck. Therefore, the probability of the second card is a red is

Then the probability of getting first is a heart and the second is a diamond card without replacement is

The probability that first is a heart and the second is diamond card without replacement is