Probability
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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.
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"?
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Answers 2 questions on probability calculations.
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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.
(a) both will fail?
We have to calculate the probability that the first and second alternators both fail.
The probability of failure of the first alternator is independent of the failure of secon dalternator.
Therfore, the failure events are independent events and we will multiply the probabilities
For independent events A and B
P(A and B) = P(A) x P(B)
probability of failure=p= 0.02
therefore , probability of not failing=(1-p)= 0.98 = 1- 0.02
Probability that both alternators will fail = probability of failure of first alternator x probability of failure of second alternator = 0.0004 =0.02 x 0.02
Answer: probability= 0.0004 or 1 in ...
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