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 0.019. (a) what is the probability that both will fail? (round your answer to 4 decimal places.) probability (b) what is the probability that neither will fail? (round your answer to 4 decimal places.) probability (c) what is the probability that at least one fails? (round your answer to 4 decimal places.) probability referencesebook & resources

Answer 1

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 0.019.  

This is a binomial probability situation, since it's "pass or fail."  The prob. of failure is 0.019.  Since the alternators are separate and independent, the prob. that two will fail is the product of 0.019 and 0.019, or 3.61 to the power -4 of 10.  The latter can also be written as 0.000361.

The probability that one alternator will fail is 1-0.019, or 0.981.
The probability that neither alternator will fail is (0.981)^2=0.9624 (to four decimal place accuracy).

What is the probability that at least one fails?  This probability is equal to the complement of the probability that ONE will fail, which on the TI 84 Plus can be calculated as 1-binompdf(2,0.981,0), which comes out to 0.000361.