Kevin's sock drawer contains 6 white socks, 4 black socks, 3 grey socks, and 5 red socks. If Kevin randomly picks two socks, what is the probability that they are both white?

The probability of Kevin choosing a white sock on the first pick, there are 6 white socks and 18 socks total so the chances are 6/18. But 6/18 simplified is 1/3. On the second choice he has to pick another sock and there are 5 left out of 17 socks total remaining. So the chances of him picking another sock are 5/17. If you multiply 1/3 by 5/17 you will end up with your answer, 5/51.

MrRoyal MrRoyal · Answer 2 · 2021-11-04T11:51:49+01:00

Probabilities are used to determine the chances of an event.

The given parameters are:

[tex]\mathbf{White = 6}[/tex]

[tex]\mathbf{Black = 4}[/tex]

[tex]\mathbf{Grey = 3}[/tex]

[tex]\mathbf{Red = 5}[/tex]

So, the total is:

[tex]\mathbf{Total = 6 + 4 + 3 + 5}[/tex]

[tex]\mathbf{Total = 18}[/tex]

The probability that both selections are white socks is:

[tex]\mathbf{Pr = \frac{White}{Total} \times \frac{White - 1}{Total - 1} }[/tex]

1 is subtracted from the fractions of the second factor, because it is a selection without replacement.

So, we have:

[tex]\mathbf{Pr = \frac{6}{18} \times \frac{6 - 1}{18 - 1} }[/tex]

[tex]\mathbf{Pr = \frac{1}{3} \times \frac{5}{17} }[/tex]

So, we have:

[tex]\mathbf{Pr = \frac{5}{51} }[/tex]

Hence, the probability that both selections are white socks is 5/51