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 =
`(4)/(8)= (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 =
`(4)/(8)= (1)/(2)`

And

Probability of pulling a red sock from the bag the third time =
`(4)/(8)= (1)/(2)`

Therefore, the probability of pulling a red sock 3 times from the bag =
`(1)/(2)* (1)/(2)* (1)/(2)= (1)/(8)`