A buyer for a large metropolitan department store must choose two firms from the four available to supply the store's fall line of men's slacks.

The buyer has not dealt with any of the four firms before and considers their products equally attractive. Unknown to the buyer, two of the four firms are having serious financial problems that may result in their not being able to deliver the fall line of slacks as soon as promised. The four firms are identified as G, and G, (firms in good financial condition) and P, and P, (firms in poor financial condition). Sample points identify the pairs of firms selected. If the probability of the buyer's selecting a particular firm from among the four is the same for each firm, the sample points and their probabilities for this buying experiment are those listed in the following table.

Sample Points Probability GIG: 96 G,P, 76 G,P2 96 G2p1 96 GzP2 96 P,pz 1/6 We define the following events:

A:(At least one of the selected firms' is in good financial condition]

B: (Firm P, is selected]

a. Define the event AnB as a specific collection of sample points.

b. Define the event AUB as a specific collection of sample points.

C. Define the event AC as a specific collection of sample points.

d. Find P(A), P(B), P(AnB). P(AUB), and P(Ac

)

by summing the probabilities of the appropriate sample points.

e. Find P(AUB) using the additive rule. Are events A and B mutually exclusive? Why?