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# Continuous Probability Distribution - Independent Events

5.62 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.

5.70 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"?

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5.62 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.

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(a) both will fail?

We know that the probability that one will fail is 0.02. The two alternators are independent of one another. The probability that both will fail is found by multiplying the individual probabilities together:

(0.02)(0.02) = 0.004

The probability that both will fail is 0.004.

(b) neither ...

#### Solution Summary

The solution shows how to determine the probability in each of the conditions and answer questions based on the determined probability.

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