Question

A bag contains 4 tan socks and 7 grey socks. emily reaches into the bag and randomly selects two socks without replacement. what is the probability that emily will get different-colored socks?

Answer 1

Tan socks = 4
Grey socks = 7
Total number of socks = 4+7 = 11 socks
Probability of picking a tan sock then grey sock:
P(T)*P(G) = (4/11)*(7/10) = 14/54

Probability of picking a Grey sock then Tan sock
P(G)*P(T) = (7/11)*(4/10) = 14/55

Probability of two different colored socks
P(T&G)+P(G&T) = (14/55)+(14/55) = 28/55