A drawer contains 5 blue socks and 5 white socks. Two socks are randomly selected from the drawer.
Q: What is the probably that the two socks are different color?
Is finding this probably the same as finding the probability that the 2 socks are the same color? I was able to find that probability but had a hard time finding it:
- $S_1$: White sock $S_1^C$: Blue
- $S_2$: white sock $S_2^C$: Blue
$P(S_2\mid S_1)\cdot P(S_1)+P(S_2^C\mid S_1^C)\cdot P(S_1^C) =
(4/9)\cdot (1/2)+(4/9)\cdot (1/2)= 4/9$
Best Answer
From 10 socks you are choosing 2, so you have $\binom{10}{2}$ possibilities. And to two socks to be different color you have to pick one blue and one white so you have $\binom{5}{1}\binom{5}{1}$ possibilities. So the final result is $\frac{25}{45}=\frac{5}{9}$.