a.Suppose the 9 people available for a committee are 3 Assistant Professors, 4 A

Question

a.Suppose the 9 people available for a committee are 3 Assistant Professors, 4 Associate

Professors, and 2 Professors. How many possible committees of size 3 can be created if we

must have 1 Assistant Professor, 1 Associate Professor, and 1 Professor?

b. A bin of batteries has three different brands. There is a 10% chance that Brand A lasts over

50 hours, 40% chance that Brand B lasts over 50 hours, and 90% chance that Brand C lasts

over 50 hours. Suppose there are 20 Brand A batteries, 30 Brand B batteries, and 10 Brand

C batteries in a bucket. What is the probability that a randomly chosen battery from the

bucket will last over 50 hours?

Explanation / Answer

A) no of ways = 3C1 * 4C1 * 2C1 = 3 * 4 * 2 = 24

B) Probability = 20 /60 * 0.1 + 30 /60 * 0.4 + 10/60 * 0.9 = 0.383

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