Question

A drawer contains 8 white and 2 black socks. two socks are randomly selected from the drawer. what is the probability they are the same color?

Answer 1

You can draw a probability tree to work thus out.

First work out the probability for getting 2 whites in a row.

It is the number of whites divided by the overall number of socks so 8/10.

Then, work the probability of doing it for a second time. This is 7/9 since you took away a sock.

Now multiply 8/10 x 7/9 so 56/90.

56/90 is the probability of getting two whites in a row, but you now need to work out the probability of two blacks.

By the same process, you can work out that the calculation is 2/10 x 1/9, so 2/90.

To work out the total probability of two of the same colour, you add the probabilities of 2 whites and 2 blacks, so it is 56/90 + 2/90, so 58/90, which can be simplified to 29/45.

Your final answer is 29/45.