Question

Your sock drawer is a mess! Although the socks are all mixed up you know you have 5 black socks, 5 stripped socks, 9 polka dot socks, 11 white socks, 5 blue socks, and one sock with pictures of little socks printed all over it. To impress your date you’re hoping to wear a pair of matching socks to school on Friday. If you take one sock out of your drawer, do not replace it and then take out another sock what is the probability that you will select a pair of polka dot socks

Answer 1

First, we need to figure out how many socks are in the drawer.

5 black socks + 5 striped socks + 9 polka dot socks + 11 white socks + 5 blue socks + 1 sock with photos of small socks = 36 socks

Pay attention to the polka dot socks now. There are 9 polka dot socks in the drawer; the odds of picking one on the first draw are 9/36 socks.

If we don't replace the first sock and draw again, there will be 8 polka dot socks remaining out of a total of 35 socks in the drawer.

As a result, the likelihood of picking a second polka dot sock after selecting the first is 8/35.

To calculate the likelihood of picking a pair of polka dot socks, multiply the odds of selecting a polka dot sock on the first draw by the probability of selecting another polka dot sock on the second draw.

The probability of choosing a pair of polka dot socks is (9/36) x (8/35) = 0.0571, or approximately 5.71%.