A sock drawer contains eight navy blue socks and five black socks with no other
socks. If you reach in the drawer and take two socks without looking and without
replacement, what is the probability that the colors of the two socks will match?

Question

Eli Assouline · Accepted Answer

Probability P(match)#=19/39# P(match)=P(blue, blue)+P(black,black) P(match)#=8/13*7/12+5/13*4/12=19/39# Have a nice day !! from the Philippines..

Julia Adams · Answer

undefined To find the probability that the colors of the two socks will match, you need to consider two cases: picking two navy blue socks or picking two black socks.

For picking two navy blue socks: $ \frac{8}{13} \times \frac{7}{12} $

For picking two black socks: $ \frac{5}{13} \times \frac{4}{12} $

Add the probabilities of the two cases together to get the total probability:

$$ \frac{8}{13} \times \frac{7}{12} + \frac{5}{13} \times \frac{4}{12} = \frac{56}{156} + \frac{20}{156} = \frac{76}{156} = \frac{19}{39} $$

So, the probability that the colors of the two socks will match is $ \frac{19}{39} $.

A sock drawer contains eight navy blue socks and five black socks with no other socks. If you reach in the drawer and take two socks without looking and without replacement, what is the probability that the colors of the two socks will match?