Question

A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a one-hour flight is 0.037.What is the probability that both will fail? .0014What is the probability that neither will fail?What is the probability that at least one fails?

Answer 1

Probability (Both fail) = 0.001369

Probability (None fails) =0.927369

Probability (at least one fails) = 0.072631

Explanation:

given data

Probability (fail) P = 0.037

two alternators is independent

solution

we get here first probability that both will fail will be

Probability (Both fail) = 0.045² ................1

Probability (Both fail) = 0.001369

and

now we get probability that neither will fail

Probability (None fails) = (1-0.037)² ...............2

Probability (None fails) =0.927369

and

now we get probability that at least one fails

Probability (at least one fails) = 1 - Probability (non fails) .................3

Probability (at least one fails) = 1 - 0.927369

Probability (at least one fails) = 0.072631