An online article (beauty.about.com) by Julyne Derrick, “Shelf Lives: How Long Can You Keep Makeup,” suggests that eye shadow and eyeliner each have a shelf life of up to three years. Suppose the shelf lives of these two products are exponentially distributed with an average shelf life of one year.
a. Calculate the probability that the shelf life of eye shadow will be longer than three years.
b. Determine the probability that at least one of these products will have a shelf life of more than three years.
c. Determine the probability that a purchased eyeliner that is useful after one year will be useful after three years.