# A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that neither will fail?

Apr 18, 2017

The probability is $P \left(A\right) = 0.9604$. See explanation.

#### Explanation:

The probability that the single alternator will NOT fail is:

$p = 1 - 0.02 = 0.98$

To calculate the probability that neither of 2 alternators fails we have to square the probability for a single alternator:

$P \left(A\right) = {p}^{2} = {0.98}^{2} = 0.9604$