Question
Asked Sep 12, 2019
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Seventy percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, 60% have an emergency locator, whereas 90% of the aircraft not discovered do not have such a locator. Suppose a light aircraft has disappeared.

a. If it has an emergency locator, what is the probability that it will not be discovered?

b. If it does not have emergency locator, what is the probability that it will be discovered?

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Expert Answer

Step 1

Consider D is defined as discovered a light aircraft which disappeared in certain country. And E is defined as a light aircraft which has an emergency locator.

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P(D) 0.70 P(D)1-P(D) =1-0.70 0.30 P(E D) 0.60 P(E' | D) 1-P(ED) =1-0.60 -0.40 P(E'I D') 0.90 P(E|D') 1-P(E'D') =1-0.90 =0.10

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Step 2

a)

The probability of the light aircraft which has an emergency locator but i...

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P(D'IE) PD'nE) P(D')P(E|D') P(E) P(E) P(D') P(E\ D') P(D)P(E D)+P(D')P(E\D') 0.30x 0.10 0.45 0.067

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