Question

Your sock drawer has 4 pairs of pink socks, 2 pairs of white socks, and 7 pairs of black socks. What is the probability that, if you choose at random withough replacement you choose a black pair of socks and then a white pair? a 7/78b 1/156c 1/12d 3/13

Answer 1

Given:

Number of pink socks = 4 pairs

Number of white socks = 2 pairs

Number of black socks = 7 pairs

Let's find the probability that if you choose at random without replacement you will choose a black pair and then a white pair.

Where:

Total pairs = 4 + 2 + 7 = 13 pairs

To find the probability, we have:

$P(black\text{ first\rparen= }\frac{\text{ number of black pairs}}{total\text{ pairs}}=\frac{7}{13}$

Now, for the probability you choose a white pair next given that the black was not replaced, we have:

$P(white)=\frac{number\text{ of white pairs}}{total\text{ pairs - 1}}=\frac{2}{13-1}=\frac{2}{12}=\frac{1}{6}$

Now, for the total probability, we have:

$\begin{gathered} P=P(black\text{ first\rparen * P\lparen white next\rparen} \\ \\ P=\frac{7}{13}*\frac{1}{6} \\ \\ P=\frac{7}{78} \end{gathered}$

Therefore, the probability is 7/78.

ANSWER: a

$\frac{7}{78}$