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?

Probability (Both fail) = 0.001369

Probability (None fails) = 0.927369

Probability (at least one fails) = 0.072631

Step-by-step 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