Question

One drawer in a dresser contains 8 blue socks and 6 white socks. a second drawer contains 4 blue socks and 2 white socks. one sock is chosen from each drawer. what is the probability that they match (same color)?

Answer 1

I think the answer is $\frac{1}{12}$ but dont be mad at me if I'm wrong...

Answer 2

The probability of drawing a blue sock from the first drawer is 8/14 = 4/7.
The probability of drawing a white sock from the first drawer is 6/14 = 3/7.
The probability of drawing a blue sock from the second drawer is 4/6 = 2/3.
The probability of drawing a white sock from the second drawer is 2/6 = 1/3.
$P(blue\ blue) = \frac{4}{7}\times\frac{2}{3}=\frac{8}{21}$
$P(white\ white)=\frac{3}{7}\times\frac{1}{3}=\frac{3}{21}$
The probability that they match is therefore (8/21) + (3/21) = 11/21
The answer is 11/21.