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.

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Mathematics

Dempsey

Today, 02:30

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.

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Mariah Cardenas · Answer 1

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

Alfonso Duffy · Answer 2

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