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Goranson and Hall (1980) explain that the probability of
Chapter 3, Problem 62E(choose chapter or problem)
Problem 62E
Goranson and Hall (1980) explain that the probability of detecting a crack in an airplane wing is the product of p1, the probability of inspecting a plane with a wing crack; p2, the probability of inspecting the detail in which the crack is located; and p3, the probability of detecting the damage.
a What assumptions justify the multiplication of these probabilities?
b Suppose p1 = .9, p2 = .8, and p3 = .5 for a certain fleet of planes. If three planes are inspected from this fleet, find the probability that a wing crack will be detected on at least one of them.
Questions & Answers
QUESTION:
Problem 62E
Goranson and Hall (1980) explain that the probability of detecting a crack in an airplane wing is the product of p1, the probability of inspecting a plane with a wing crack; p2, the probability of inspecting the detail in which the crack is located; and p3, the probability of detecting the damage.
a What assumptions justify the multiplication of these probabilities?
b Suppose p1 = .9, p2 = .8, and p3 = .5 for a certain fleet of planes. If three planes are inspected from this fleet, find the probability that a wing crack will be detected on at least one of them.
ANSWER:
Solution :
Step 1 of 2:
Given the probability of detecting a crack in an airplane wing is the product of .
The probability of inspecting a plane with a wing crack is .
The probability of inspecting the detail in which the crack is located is .
Our goal is:
a). We need to find what assumption justifies the multiplication of these probabilities.
b). We need to find the probability that a wing crack will be detected on at least one of
them.
a).
Now we have to find what assumption justifies the multiplication of these probabilities.
The events corresponding to the three probabilities have to be independent and the inspection procedure is random.