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# Statistics of Airplanes Failing

# 5.62: A certain airplane has two independent alternators to provide electrical power. The probabilty 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.

a) The likelihood that the first alternator will not succeed = 0.02
The likelihood that the second alternator will not succeed = 0.02

Since the two events are independent, then the likelihood that both alternators will fail = 0.02 x 0.02 = 0.0004 (Four in ten thousand probability)

b) The probability that the first alternator will not fail = 1 - 0.02 = 0.98
The probability that the second alternator will not fail = 1- 0.02 = 0.98

Since the two events are independent, then the probability that both alternators won't fall short (neither one will pass) = 0.98 x 0.98 = 0.9604 (Over 96%)

c) Probability that one or the other will fail = 1 - probability both will not pass - likeliness that neither will fail = 1 - 0.0004 - 0.9604 = 0.0392

# 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"?

a) Likeliness of a fatal accident over a lifetime = number of trips x probability of a fatal accident per trip
= 50000x 1/4000000 = 0.0125 (or 1.25%)

the answer is based on the assumption of independence. This assumption may be debased because not all drivers have the same altitude of authority and readiness to dodge an accident. The younger drivers are more likely to have a car accident verses more adult drivers who are in their prime i.e. 30's and mid 40's. Wearing a seat belt will also help reduce the number of fatalities if an accident is to occur.

b) A driver may be tempted not to put their seat belt on since they may presume that there is a very minute chance of having a deadly accident based on the numbers above. However, the driver should be conscious that many deadly accidents are caused by accidents where drivers were not wearing seat belts.

#### Solution Preview

# 5.62: A certain airplane has two independent alternators to provide electrical power. The probabilty 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.

a) The likelihood that the first alternator will not succeed = 0.02
The likelihood that the second alternator will not succeed = 0.02

Since the two events are independent, then the likelihood that both alternators will fail = 0.02 x 0.02 = 0.0004 (Four in ten thousand probability)

b) The probability that the first alternator will not fail = 1 - 0.02 = 0.98
The probability that the second alternator will not fail = ...

#### Solution Summary

The statistics of airplanes failing are examined.

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