Two cards are drawn from a standard deck without replacement. What is the probability that the first card is a club and the second card is red? (Round your answer to three decimal places.)
Question
Two cards are drawn from a standard deck without replacement. What is the probability that the first card is a club and the second card is red? (Round your answer to three decimal places.)
Solution
Sure, let's break this down:
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A standard deck has 52 cards: 13 each of clubs, diamonds, hearts, and spades.
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The probability of drawing a club as the first card is 13 out of 52, or 1/4.
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After drawing one card, there are now 51 cards left. The red cards are the diamonds and hearts, which total 26 cards. So, the probability of drawing a red card as the second card is 26 out of 51.
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The probability of both events happening is the product of their individual probabilities. So, the probability that the first card is a club and the second card is red is (1/4) * (26/51).
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To get the final answer, calculate this product and round to three decimal places.
Let's calculate:
(1/4) * (26/51) = 0.12745
So, the probability that the first card is a club and the second card is red is approximately 0.127 or 12.7%.
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