Bookmark Seventy-four percent of the light aircraft that disappear while in flig

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Seventy-four percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, 62% have an emergency locator, whereas 89% of the aircraft not discovered do not have such a locator. Suppose a light aircraft has disappeared. (Round your answers to three decimal places.)

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


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

Explanation / Answer

P(discovered)= 0.74 and P(not discovered)=1-0.74=0.26

P(emergency locator| discovered)=0.62, P(no locator| discovered)=1-0.62=0.38

P(no locator|not discovered)=0.89, P(emergency locator | not discovered)=1-0.89=0.11

P(emergency locator)=P(emergency locator| discovered)*P(discovered)+P(emergency locator | not discovered)*P(not discovered)=0.62*0.74+0.11*0.26=0.487

P(no locator)=1-0.487=0.513

a) P(not discovered|emergency locator)=P(emergency locator | not discovered)*P(not discovered)/P(emergency locator) =0.11*0.26/0.487=0.0587

b) P(discovered| no locator)=P(no locator | discovered)*P(discovered)/P(no locator)

=0.38*0.74/0.513

=0.548

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