The employees at a computer manufacturer own US, German and Japanese cars, with

Question

The employees at a computer manufacturer own US, German and Japanese cars, with about 50% of them being US and 35% Japanese. 60% of Japanese cars would be classified as compact as would 40% of German cars and only 20% of US cars. Assume that these employees spread their purchases randomly across all models of all cars. a. Estimate the probability that the first car coming into the parking lot in the morning is a compact car. b. Assuming it is a compact estimate the probability that it is a Japanese car. c. Estimate the probability that the first three cars in the lot come from different continents. (Adapted from a textbook) Suppose that a certain department has 3 unbuffered terminals that can be connected to a computer via 2 communication lines. Terminal 1 has its own leased line while terminals 2 and 3 share a leased line so only one may be in use at a time. During the work day terminal 1 is in use 30 minutes of each hour, terminal 2 is in use 10 minutes of each hour and terminal 3 is in use 5 minutes of each hour, all times being average times. a. Assuming that the communication lines operate independently what is the probability that at least one terminal is in operation at a random time during the working day? b. If the operation of the two lines is not independent with the conditional probability that terminal 2 is in use given that terminal 1 is in operation equal to 1/3, and the corresponding conditional probability that terminal 3 is in use equal to 1/12, what is the probability that at least one line is in use?

Explanation / Answer

(5)

(a) Probability = 37/100 = 0.37

(b) Probability = (21/100)/(37/100) = 0.5676

(c) Probability = 0.50 * 0.15 * 0.35 = 0.0263.

US G J Total C 20% of 50 = 10 40% of 15 = 6 60% of 35 = 21 37 NC 50 - 10 = 40 15 - 6 = 9 35 - 21 = 14 63 Total 50 15 35 100

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