# A certain airplane has two independent alternators to provide electrical power.

Prepare answers to the following assignments from the e-text, Applied Statistics in Business and Economics, by Doane and Seward:

Chapter 5 - Chapter Exercises 5.62 and 5.70

Note: Methods of computation could include the usage of Excel, SPSS, Lotus, SAS, MINITAB, or by hand computation.

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 the steps

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 the 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"?

#### Solution Preview

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 the steps

Solution.

Denote by E1 and E2 the events that alternators A and B will fail on a 1- hour flight, respectively. Then E1-bar and E2-bar denote the events that alternators A and B will NOT fail on a 1- hour flight, respectively. We know that E1 and E2 are independent, and P(E1)=P(E2)=0.02. So, P(E1-bar)=1-P(E1)=0.98; P(E2-bar)=1-P(E2)=0.98

(a) The probability that both will fail is equal to P(E1 and E2). Note that E1 and E2 are ...