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  4. An aircraft has three engines A, B and C. The aircraft crashes if all the three engines fail. The probabilities of failure are 0.03, 0.02 and 0.05 for engines A, B and C respectively. What is the probability that the aircraft will not crash?

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Q. An aircraft has three engines A, B and C. The aircraft crashes if all the three engines fail. The probabilities of failure are 0.03, 0.02 and 0.05 for engines A, B and C respectively. What is the probability that the aircraft will not crash?

Probability - Part 2

Solution:

Since, probabilities of failure for engines A, B and C
P (A), P(B) and P(C) are 0.03, 0.02 and 0.05 respectively.
The aircraft will crash only when all the three engine fail.
So, probability that it crashes = P(A). P(B). P(C)
= 0.03 $\times$ 0.02 $\times$ 0.05
= 0.00003
Hence, the probability that the aircraft will not crash, = 1 - 0.00003= 0.99997