Question

Seventy-five 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 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?

Answer 1

Explanation:

Given 75% of Light aircraft discovered that were disappeared

Also out of 75% 62% had an emergency locator

so remaining 25 % were not discovered

out of not discovered 83% do not had locator

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

`P\left [(not\ discovered)/(emergency\ locator)\right ]`=
`(0.25* 0.17)/(0.25* 0.17+0.75* 0.62)`

`P\left [(not\ discovered)/(emergency\ locator)\right ]`=0.0837

(b)
`P\left [(discovered)/(does\ not\ have\ locator)\right ]`=
`(0.75* 0.38)/(0.75* 0.38+0.25* 0.83)`

`P\left [(discovered)/(does\ not\ have\ locator)\right ]`=0.5786