Question

You have a bag with 4 pairs of socks. There are 2 red pairs and 2 black pairs. You pull a sock from the bag and put it back 3 times. What is the probability that you pull out a red sock each time?

Answer 1

Total Number of socks = 4 pairs= 8 socks
Number of red socks = 4
Number of black socks = 4

Probability of pulling a red sock from the bag the first time =  $\frac{4}{8}= \frac{1}{2}$

Since the sock is placed back in the bag before pulling a sock again, the number of socks remains the same.

So,

Probability of pulling a red sock from the bag the second time =  $\frac{4}{8}= \frac{1}{2}$

And

Probability of pulling a red sock from the bag the third time =  $\frac{4}{8}= \frac{1}{2}$

Therefore, the probability of pulling a red sock 3 times from the bag = $\frac{1}{2}* \frac{1}{2}* \frac{1}{2}= \frac{1}{8}$