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 0.02. a) What is the probability that both will fail? b) Neither will fail? c) One or the other will fail?

A. 0.0004, 0.9604, ?
B. 0.0004, 0.9604, 0.0396
C. 0.02, 0.98, ?
D. 0.02, 0.98, 0.04

Answer 1

To find the probabilities, we consider the independent failure chances of two airplane alternators. The results are: 0.0004 for both failing, 0.9604 for neither failing, and 0.0396 for one or the other failing; hence, option B is correct.

Step-by-step explanation:

The question involves calculating probabilities of independent events. Specifically, it asks about the probabilities associated with alternators on an airplane failing during a one-hour flight.

1. Both alternators failing: The probabilities multiply since the events are independent, so 0.02 × 0.02 = 0.0004.
2. Neither alternator failing: The probability of one alternator not failing is 1 - 0.02 = 0.98. Hence, the probability of both not failing is 0.98 × 0.98 = 0.9604.
3. One or the other alternator failing: This can occur in two ways: the first alternator fails and the second doesn't, or the first doesn't fail and the second does. This gives us (0.02 × 0.98) + (0.98 × 0.02) = 0.0396.

The correct option is therefore B: 0.0004, 0.9604, 0.0396.