Question

Kevin is trying to find a brown sock in his drawer. He has 16 white socks, 4 brown socks, and 6 black socks. What is the probability that he pulls out either a black or white sock, puts it back and then pulls out a brown sock?

Answer 1

The probability that he pulls out either a black or white sock, puts it back and then pulls out a brown sock is $(\frac{22}{169} )$

Step-by-step explanation:

Here , as given the total number of:

White Socks  = 16

Brown Socks = 4

Black socks  = 6

So, the total number of socks in the drawer   = 16 + 4 + 6 = 26 socks

Now, the probability of picking a sock either a black or white sock is

$= \frac{\textrm{Total number of black + white sock}}{\textrm{The total number of socks}} = \frac{16+6}{26} = \frac{22}{26} = \frac{11}{13}$

Also, the picked sock is replaced. So, now the total socks are same = 26.

the probability of picking a brown sock is

$= \frac{\textrm{Total number of brown sock}}{\textrm{The total number of socks}} = \frac{4}{26} = \frac{2}{13}$

Now, since both events are independent events , so the combined probability is given as:

P (E) = $(\frac{11}{13} )\times (\frac{2}{13} ) = (\frac{22}{169} )$

Hence, the probability that he pulls out either a black or white sock, puts it back and then pulls out a brown sock is $(\frac{22}{169} )$