Question

There are 10 brown socks and 8 blue socks in a drawer. In the dark, you pull out a sock and put it on. Then you pull out another sock and put it on your other foot. What is the probability that you have on two blue socks?

Answer 1

The probability of pulling out two blue socks in the dark is 68/153.

Step-by-step explanation:

To find the probability of getting two blue socks, we need to consider two scenarios:

Scenario 1: The first sock withdrawn is blue.

There are 8 blue socks and a total of 18 socks (10 brown + 8 blue) to choose from in the first draw. After putting the first blue sock on, there are now 7 blue socks and a total of 17 socks remaining for the second draw. Therefore, the probability of getting two blue socks in this scenario is (8/18) x (7/17).

Scenario 2: The first sock withdrawn is brown.

There are 10 brown socks and a total of 18 socks to choose from in the first draw. After putting the first brown sock on, there are still 8 blue socks and a total of 17 socks remaining for the second draw. Therefore, the probability of getting two blue socks in this scenario is (10/18) x (8/17).

To find the overall probability, we need to add the probabilities of each scenario:

(8/18) x (7/17) + (10/18) x (8/17) = 56/306 + 80/306 = 136/306 = 68/153.

Answer 2

28 / 153 or around an 18.3% chance.

Step-by-step explanation:

P (b, b) = (total blue / total socks) × (total blue – 1 / total socks – 1) =

(8 / 18) × (7 / 17) = 56 / 306 = 28 / 153