You randomly draw two cards from a normal deck of 52 cards. What is the probability that the first card is a heart and the second card is not a diamond if you do not replace the first card?

Answer 1

The probability that a heart will be drawn on the first pick is 13/52 = 1/4

The probability of drawing a diamond on the second pick is 13/51 ( heart card not replaced)

The probability of not picking a diamond on the second pick is 1- (13/51) = 38/51

So, the probability of both is (1/4)(38/51) = 38/204