Individual Exercises Week Four
Questions: 5.62
A certain airplane has 2 independent alternators to provide electrical power. The hazard that a precondition alternator go away rat on a 1-hour flight is .02. What is the probability that (a) two will fail? (b) Neither will fail? (c) One or the other will fail? assign all steps carefully.
Answer: N = 2, p = .02, a = alternator 1, b = alternator 2
A) Both will fail
(.02)(.02) = 0.0004, Probability that both will fail is 0.0004 or 0.04%
B) 1-( Pa + Pb) + (P(both fail)) = (1 - 0.04) + 0.0004 = 0.9604
Neither will fail is 0.9604 or 96.04%
C) Pa + Pb (P(both fail)) = 0.02 + 0.02 0.0004 = 0.0396
One or the other will fail is 0.0396 or 3.96%
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Questions: 5.70
The probability is 1 in 4,000,000 that a single auto elusion in the United States will result in a sinisterity. oer a lifetime, an average U.S. driver takes 50,000 jaunts. (a) What is the probability of a fatal accident everyplace a lifetime? Explain your think carefully. Hint: Assume independent events. Why might the self-assertion of independence be violated? (b) Why might a driver be tempted not to use a spot belt just on this trip?
N = 2, p = 0.
00000025 (1/4,000,000), a = fatal accident, b = no fatal accident
P (a fatal accident over a lifetime) = 1 - P (NO fatal accident over a lifetime)
Pa = 1 Pb
Pa = 1 0.00000025
Pa = 0.99999975 ^ 50000 = 0.987577799
Pa = 1 0.987577799
Pa = 0.012422201
Probability of a fatal accident over a drivers lifetime is 0.012422201 (1.24%).
The assumption of independence is violated because drivers do not go the homogeneous route or the same distance for every single trip. They could take a firm trip to the store, or go on a trip across the country. The drivers themselves are not the same for each trip either. The driver could be not feeling well, could be intoxicated, or their driving habits might...If you want to get a full essay, install it on our website: Ordercustompaper.com
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