1. An office building contains three unreliable elevators A, B and C, which are down 35%, 30% and 10%

of the time, respectively.

(a) Let A, B and C denote the events in which elevators A, B and C are down, respectively. Describe

the following events by taking unions, intersections, and/or complements of A, B and C.

All three elevators are down.

Elevator A is down, but not B or C.

None of the elevators is down.

At least one elevator is down.

Exactly one elevator is down.

(b) What are the maximum and minimum possible values for P(A [ B [ C)?

2. Consider the sample space S = {0; 1; 2}. Suppose P(0) = 1/3 and P(1) = 2 * P(2). Let A denote the event {0; 1}. Compute P(A).

3. Suppose a box contains five balls of exactly the same size, shape and feel. Three of these balls are red

and the other two are green. Choose two balls, one after another, without replacement (that is, you

do not put the first ball back into the box after selection).

(a) What is the probability that the first ball is red?

(b) What is the probability that the second ball is green?

(c) What is the probability that both balls are of the same color?