The major airline industry is subject to labor strikes by the pilots, the mechan

Question

The major airline industry is subject to labor strikes by the pilots, the mechanics, the flight attendants, or by two or more of these three labor groups. Using the following notations: A = strike by the pilots B = strike by the mechanics C strike by the flight attendants Determine the probabilities of a labor strike in the major airline industry. Assume that the following respective probabilities of strikes by the three industrial groups: P(A) 0.03, P(B) 0.05, P(C)-0.05, and that strikes by the different labor groups are statistically independent.

Explanation / Answer

The probability of a labor strike = P(A U B U C)

P(A) = 0.03 P(B) = 0.05 P(C) = 0.05

Since the events are statistically independent,

P(A B) = P(A) P(B) = 0.03 * 0.05 = 0.0015

P(B C) = P(A) P(B) = 0.05 * 0.05 = 0.0025

P(A C) = P(A) P(B) = 0.03 * 0.05 = 0.0015

P(A B C) = P(A) P(B) P(C) = 0.03 * 0.05 * 0.05 = 0.000075

P(A U B U C) = P(A) + P(B) + P(C) - P(A B) - P(B C) - P(A C) + P(A B C)

= 0.03 + 0.05 + 0.05 - 0.0015 - 0.0025 - 0.0025 + 0.000075

= 0.123575.

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