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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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) About Me  (Show Source):
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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