A certain airplane has two independent alternators to provideelectrical power. T

Question

A certain airplane has two independent alternators to provideelectrical power. The probability that a given alternatorwill fail on a 1-hour flight is .02. What is the probabilitythat (a) both will fail? (b) neither will fail? (c) One or the other will fail? Show all steps carefully. Any assistance is appreciated. A certain airplane has two independent alternators to provideelectrical power. The probability that a given alternatorwill fail on a 1-hour flight is .02. What is the probabilitythat (a) both will fail? (b) neither will fail? (c) One or the other will fail? Show all steps carefully. Any assistance is appreciated.

Explanation / Answer

given that probability that a given alternator will fail is, p1=0.02 probability that a given alternator will fail is,p2=0.02 a)probability that both will fail , 0.02*0.02= 0.0004 b) neither fail = (1-p1)*(1-p2)                    = 0.98*0.98                    = 0.9604 c) one or other will fail                          p1(1-p2)+p2(1-p1)                        = 0.02 *0.98 + 0.02*0.98                         =0.0392 probability that a given alternator will fail is,p2=0.02 a)probability that both will fail , 0.02*0.02= 0.0004 b) neither fail = (1-p1)*(1-p2)                    = 0.98*0.98                    = 0.9604 c) one or other will fail                          p1(1-p2)+p2(1-p1)                        = 0.02 *0.98 + 0.02*0.98                         =0.0392

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