Question

Patrick is doing a card trick using a standard 52-card deck with four suits: hearts, diamonds, spades, and clubs. He shows his friend a card, replaces it, and then shows his friend another card. Give the probability that the first card is not a club and the second card is not a heart.

Answer 1

Probability that the first card is not a club is 1 minus probability that it is a club. i.e. 1 - 1/4 = 3/4
Probability that the second card is not a heart is 1 minus probability that it is a heart. i.e. 1 - 1/4 = 3/4
Probability that the first card is not a club AND the second card is not a heart is 3/4 x 3/4 = 9/16

Answer 2

There are a total of 52 cards in a deck- that is 4 cards for each shape: heart, diamond, spade and club and 13 numbers. There are thus, 13 cards with club shape and 13 cards with a heart shape. Hence the probability that the first card is not a club is (52-13)/52 = 3/4  and the second card is not a heart (51-13)/51 = 38/51 is equal to 3/4 *38/51 equal to 19/34