A man has two pairs of shoes: one black pair and one brown pair. He also has five pairs of socks: black, white, blue, yellow, and grey. One day, he randomly selects a pair of shoes and a pair of socks to wear. What is the theoretical percentage probability that the man will wear brown shoes and either grey, white, or yellow socks?

 Jun 6, 2020

This is just a matter of probability. Let's look at the shoes first. He only has two pairs, so if he chooses one at random, there is a 50% chance it will be brown and 50% it will be black. 50% he will choose the shoes asked in the problem. Now let's look at the socks. The problem asks if he wears any 3 of 5 socks, so there is a 60% he will choose one of the socks asked in the problem. 


We can write this out as fractions: 1/2 - shoes. 3/5 - socks. To get them together, you need to multiply them together. 


1/2 * 3/5 = 3/10. So the answer is 30%

 Jun 6, 2020
edited by Arcee30  Jun 6, 2020

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