Seventy-four percent of the light aircraft that disappear while in flight in a c

Question

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, 64% have an emergency locator, whereas 84% 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

a)P(emergency locator)=P(discovered and emergency locator)+P(not discovered and emergency locator)

=0.74*0.64+(1-0.74)*(1-0.84)=0.5152

hence P(not discovered|emergency locator)=

=P(not discovered and emergency locator)/P(emergency locator)=(1-0.74)*(1-0.84)/0.5152

=0.081

b)

P(discovered|no emergency locator)=0.74*0.36/(1-0.5152)=0.550

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