Ten red cards and ten black cards are placed in a bag. You choose one card and then another without replacing the first card. What is the probability

SchachtN

SchachtN

Answered question

2021-05-31

Ten red cards and ten black cards are placed in a bag. You choose one card and then another without replacing the first card. What is the probability that the first card will be red and the second card will be black?

Answer & Explanation

Aniqa O'Neill

Aniqa O'Neill

Skilled2021-06-01Added 100 answers

The events are dependent because the outcome of drawing the first card affects the outcome of the next draw. With two dependent events A and B, we also apply the Multiplication Rule:
P(A then B)=P(A)P(B after A)
The probability that the first draw is a red card is 38=3. The probability that the second draw is a black card is now 48 (since there is no replacement). Hence, the probability of first drawing red card then a black is:
P(red then black)=P(red)P(black after red)
(ved thon black) = 121019
P(red then black) = 519

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