A special deck of cards has 10 cards that are clubs and 10 cards that are hearts. A card is chosen from the deck. It is then replaced, and a second card is chosen from the deck. What is P(at least one card is a heart)? three fourths one half one fourth 1 over 26

Please Answer soon I can only open and take this exam once and I only have a couple hours before it closes out.

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anngriselda2021 anngriselda2021

17-05-2024
Mathematics

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A special deck of cards has 10 cards that are clubs and 10 cards that are hearts. A card is chosen from the deck. It is then replaced, and a second card is chosen from the deck. What is P(at least one card is a heart)? three fourths one half one fourth 1 over 26

Please Answer soon I can only open and take this exam once and I only have a couple hours before it closes out.

Answer :

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adeletedaccount adeletedaccount · Answer 1 · 2024-05-17T19:12:46-04:00

ok so the deck has 10 clubs and 10 hearts. if we pick a card, replace it, then pick again, we want to find the probability that at least one of the two cards is a heart. it's easier to first find the probability that **neither** card is a heart and then subtract from 1.

probability that the first card is a club = 10/20 = 1/2

probability that the second card is a club (since the card is replaced) = 1/2

so the probability that both cards are clubs = (1/2) * (1/2) = 1/4

therefore, the probability that at least one card is a heart = 1 - probability that both cards are clubs = 1 - 1/4 = 3/4

Answer :

so the answer is three fourths.

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