I need assistance with the following problems:

Problem 1:

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 (a) both will

fail? (b) Neither will fail? (c) One or the other will fail? Show all steps carefully.

Mr F says: Drawing a tree diagram is a simple approach to take.

Problem # 2

The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a

fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of

a fatal accident over a lifetime? Explain your reasoning carefully.

*Hint: *Assume independent

events. Why might the assumption of independence be violated? (b) Why might a driver be

tempted not to use a seat belt “just on this trip”?