Given a standard deck of cards, what is the probability that you choose a red card then choose a heart, assuming you replace the first card?

Answer 1

In a standard deck of cards there are 52 cards, half of which are red, half are black.

Also, there are 4 suits, clubs (♣), diamonds (♦), hearts (♥) and spades (♠), each of which has 13 cards.

So the probability of getting a red card is 26/52 = 1/2.

Because we replace the first card, there will be 52 cards in the deck before the second selection.

The probability to pick a heart (which is a suit) is 13/52 = 1/4.

For the two subsequent selection we multiply the probabilities, so your final answer is 1/2 * 1/4 = 1/8.