Seventy-one percent of the light aircraft that disappear while in flight in a ce

Question

Seventy-one percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, 65% have an emergency locator, whereas 83% 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

Seventy-one percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, 65% have an emergency locator, whereas 83% of the aircraft not discovered do not have such a locator. Suppose a light aircraft has disappeared. (Round your answers to three decimal places.)

D=discovered   Dc= not discovered

L=located   Lc = not located

P(D)=0.71       P(Dc) =0.29

P(L/D)=0.65     P(Lc/D) =0.35

P(Lc/ Dc)=0.83     P(L/ Dc) =0.17  

Baye’s theorem is used

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

P(Dc/L) = P(L/Dc) P(Dc) / (P(L/Dc) P(Dc)+ P(L/D) P(D))

            =0.17*0.29 / (0.17*0.29+0.65*0.71)

=0.0493/0.5108 =0.0965

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

P(D/Lc) = P(Lc/D) P(D) / (P(Lc/D) P(D)+ P(Lc/Dc) P(Dc))

=0.35*0.71 / (0.35*0.71+0.83*0.29)

=0.2485/0.4892

=0.508

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