Question

Suppose Mike has a dresser with 3 tan pants, 5 jeans, 2 black pants, and 3 gray pants. He also has 2 brown shoes, 3 black shoes, and 2 blue shoes. If he randomly chooses a pair of pants and shoes, what is the probability that both are black? Give your answer as an exact fraction and reduce the fraction as much as possible.

Answer 1

Probability of choosing a black pair of pants and shoes
`= (6)/(91)`

Explanation:

Given:

Total number of pants Mike has =
`\textrm{ 3 tan pants + 5 jeans + 2 black pants + 3 gray pants = 13 pair of pants}`

Probability of randomly choosing a pair of black pants =
`\frac{\textrm{Number of Black pants}}{\textrm{Total number of pants}} = (2)/(13)`

Total number of shoes Mike has =
`\textrm{ 2 brown shoes + 3 black shoes + 2 blue shoes = 7 pairs of shoes}`

Probability of randomly choosing a pair of black shoes =
`\frac{\textrm{Number of Black shoes}}{\textrm{Total number of shoes}} = (3)/(7)`

Probability of choosing a black pair of pants and shoes =
`(2)/(13)* (3)/(7) = (6)/(91)`