Question

Your sock drawer contains 10 pairs of white socks and 4 pairs of black socks. You reach in and pull out two pairs of socks in a row, without replacement. Show Work.

1. What is the probability that the second pair is white, given that the first pair is black?
2. What is the probability that the second pair is white, given that the first pair is white?
3. What is the probability that the second pair is black, given that the first pair is black?
4. What is the probability that the second pair is black, given that the first pair is white.

Answer 1

probability that the second pair is white, given that the first pair is black

=10/13 (since if first pair is black, there remains 10 white pair out of remaining 13 pairs)

probability that the second pair is white, given that the first pair is white =9/13

(since if first pair is white , there remains 9 white pair out of remaining 13 pairs)

probability that the second pair is black, given that the first pair is black =3/13

(if first pair is black, there remains 3 black pair out of remaining 13 pairs)

probability that the second pair is black, given that the first pair is white =4/13

(if first pair is white, there remains 4 black pair out of remaining 13 pairs)