Question

10 red cards and 10 and 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 1

Answer:  5/19

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Explanation:

There are A = 10 red cards out of B = 10+10 = 20 cards total.

A/B = 10/20 = 1/2 represents the probability of picking a red card.

After that card is selected, there are C = 10 black cards out of D = 20-1 = 19 cards left. The fraction C/D = 10/19 represents the probability of picking a black card where we did not put the first red card back.

Multiply the two fractions we found.

(A/B)*(C/D) = (1/2)*(10/19) = 10/38 = 5/19 is the probability of getting the first card that is red and the second card that is black.