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}}=(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}}=(2)/(13-1)=(2)/(12)=(1)/(6)`

Now, for the total probability, we have:

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

Therefore, the probability is 7/78.

ANSWER: a

`(7)/(78)`