1. In a lot of n components, 30% are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective,….

## What is the probability that the project is profitable?

1. The article “Traps in Mineral Valuations—Proceed With Care” (W. Lonegan, Journal of the Australasian Institute of Mining and Metallurgy, 2001:18–22) models the value (in millions of dollars) of a mineral deposit yet to be mined as a random variable X with probability mass function p(x) given by p(10) = 0.40, p(60) = 0.50, p(80) = 0.10, and p(x) = 0 for values of x other than 10, 60, or 80.

a. Is this article treating the value of a mineral deposit as a discrete or a continuous random variable?

b. Compute µX .

c. Compute σX .

d. The project will be profitable if the value is more than $50 million. What is the probability that the project is profitable?

2. Six new graduates are hired by an engineering firm. Each is assigned at random to one of six cubicles arranged in a row in the back of the room that houses the engineering staff. Two of the graduates are Bill and Cathy. What is the probability that they are assigned adjacent cubicles?

3. A closet contains four pairs of shoes. If four shoes are chosen at random, what is the probability that the chosen shoes do not contain a pair?