Question

Mixed in a drawer are 2 blue socks, 2 white socks, and 2 gray socks. You pull out two socks, one at a time, without looking. Find the probability of getting 2 socks of the same color.

Answer 1

Mixed in a drawer are 2 blue socks, 2 white socks, and 2 gray socks. You pull out two socks, one at a time, without looking. Find the probability of getting 2 socks of the same color.

Solution::

Here total number of socks is 8 among these 2 are blue socks, 2 are white socks, and 2 are gray socks.

If, we pull out two socks, one at a time, without looking.

Then the matching pairs are given by

{(blue, blue),(white,white),(gray,gray)}

So, there are 3 ways to get matching pairs.

P(both are blue)

=P(first is blue, second is blue)

=2/8 x 1/7

=2/56

P(both are white)

=P(first is white, second is white)

=2/8 x 1/7

=2/56

P(both are gray)

=P(first is gray, second is gray)

=2/8 x 1/7

=2/56

So, the probability of both socks are same colours is given by

P(two socks are same colours)

=P(both are blue)+P(both are white)+P(both are gray)

=2/56 + 2/56 + 2/56

=6/56

=3/28

So, the probability of both socks are same colours is 3/28