SOLUTION: Two cards are drawn in succession from a standard​ 52-card deck. What is the probability that the first card is red and the second card is black?
If the cards are drawn
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If the cards are drawn
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Question 1120481: Two cards are drawn in succession from a standard 52-card deck. What is the probability that the first card is red and the second card is black?
If the cards are drawn without replacement?
If the cards are drawn with replacement?
Type an integer or decimal rounded to four decimal places as needed. Answer by solver91311(24713) (Show Source):
The probability of a red card on the first draw is because 26 of the cards are red and there are a total of 52 cards. If you do not replace the card, then presuming you did draw a red card on the first draw, there would remain 25 red cards and 26 black cards, so the probability of drawing a black card on the second draw would be . Having accounted for the change in the number of cards, the two events are independent and the probability of both events is the product of the individual probabilities, that is . You can do your own arithmetic.
If you do replace the card, then the probability of a black card on the second draw is . And again, these are independent events so the probability of both is the product of the individual probabilities. .
John
My calculator said it, I believe it, that settles it
