Question

A designer is creating a store window display from three pairs of pants ( Brown black and blue ), 2 shirts ( Black and blue ), and 3 pairs of shoes ( Brown black and blue ) that are available to choose from. What is the probability that the outfit consists entirely of the same color if the components are chosen at random?

Answer 1

The probability that the outfit consists entirely of the same color if the components are chosen at random

= P(outfit color is black) + P(outfit color is blue)

= P(pant = black, shirt = black, shoe = black) + P(pant = blue, shirt = blue, shoe = blue)

= [P(pant = black)*P(shirt = black)*P(shoe = black) ]+ [P(pant = blue)*P(shirt = blue)*P(shoe = blue)]