Sloppy Joe has lots of socks but not all have matching pairs. He has 5 blue socks, 7 red socks, 3 white socks, and 4 green socks. It's early in the morning and dark and he doesn't want to turn on the light and wake his wife. When he randomly picks two socks from the drawer what is the probability that they match?
+23246 To get a matching pair, he will need either 2 blue socks or 2 red socks or 2 white socks or 2 green socks.
There are (5 + 7 + 3 + 4) = 19 socks.
To get 2 blue socks, he will need a blue sock (5/19) and another blue sock (4/18) = (5/19)(4/18) = 20/342.
To get 2 red socks, he will need a red sock (7/19) and another red sock (6/18) = (7/19)(6/18) = 42/342.
To get 2 white socks, he will need a white sock (3/19) and another white sock (2/18) = (3/19)(2/18) = 6/342.
To get 2 green socks, he will need a green sock (4/19) and another green sock (3/18) = (4/19)(3/18) = 12/2342.
Any of those combinations will give him a matching pair of socks, so add them:
20/342 + 42/342 + 6/342 + 12/342 = 80/342.
+23246 To get a matching pair, he will need either 2 blue socks or 2 red socks or 2 white socks or 2 green socks.
There are (5 + 7 + 3 + 4) = 19 socks.
To get 2 blue socks, he will need a blue sock (5/19) and another blue sock (4/18) = (5/19)(4/18) = 20/342.
To get 2 red socks, he will need a red sock (7/19) and another red sock (6/18) = (7/19)(6/18) = 42/342.
To get 2 white socks, he will need a white sock (3/19) and another white sock (2/18) = (3/19)(2/18) = 6/342.
To get 2 green socks, he will need a green sock (4/19) and another green sock (3/18) = (4/19)(3/18) = 12/2342.
Any of those combinations will give him a matching pair of socks, so add them:
20/342 + 42/342 + 6/342 + 12/342 = 80/342.
