Question

A sock drawer contains winter socks and summer socks. Both varieties come in two colors: red and blue. There are two pairs each of red summer socks and red winter socks, and one pair each of blue summer socks and blue winter socks. If a sock is selected randomly, what is the probability it will be a red sock or a winter sock?

A. 1/9
B. 1/3
C. 2/3
D. 5/6

(I've tried solving this problem multiple times myself and keep getting 1/3, but apparently that answer is wrong. Please help?)

Answer 1

Okay so basically there are 6 socks in total right? Because there are two of red summer and two of red winter and 1 blue summer and 1 blue winter. So 6 socks in total. How many of them are red? 4. And there is a blue WINTER sock. So 4+1=5 and since there are 6 socks the probability is 5/6

Answer 2

I thought that since it said that there were pairs, the total number of socks would be 12?

Answer 3

I don't think it matters because you would just get 10/12 and simplify that down to 5/6

Answer 4

Please show me what I am doing wrong.
8 red socks = 8/12 = 2/3
6 winter socks = 6/12 = 1/2
1/2 x 2/3 = 1/3 ?

Answer 5

@freak139

Answer 6

There aren't 6 winter socks because you already chose the red winter socks in the 8 pairs, you can't count them twice in the same pile because 8+6=14 out of 12. So when you counted the red socks correctly but since you already chose the RED winter socks, all thats left is the BLUE winter socks.
so
8 red socks + 2 blue winter socks = 10 out of 12