Your sock drawer is a mess and contains 8 white socks, 6 black socks, and 4 red socks. What is the probability that the first sock you pull out will be black and the second sock you pull out without replacing the first sock, will be black?

Mar 7, 2017

$\frac{1}{3} , \frac{5}{17}$

Explanation:

$\text{Probability of an event }$is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\left(\text{number of favourable outcomes")/("total number of possible outcomes}\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{here favourable outcome is pulling out a black sock}$ of which there are 6.

$\text{number of possible outcomes } = 8 + 6 + 4 = 18$

$\Rightarrow P \left(\text{black sock}\right) = \frac{6}{18} = \frac{1}{3}$

No replacement means there are now a total of 17 socks of which 5 will be black.

$\Rightarrow P \left(\text{2nd black sock}\right) = \frac{5}{17}$