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, 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

Facts of the problem:

74% of light aircraft disappear & are dicovered.

Therfore 26% are not discovered.

Of the 74% discovered 62% have emergency locator while 38% do not have.

From 26% of the aircraft 89% of them dont have locators while 11% have..

a)

A light aircraft has disappeared so 26% disappear and 11% have an emergency locator.

so combined probabilty of the aircraft not being discovered and not having an emergency locator is 0.62*0.11 = 0.0682= 6.82%

b)

Of the 74% discovered 62% have emergency locator while 38% do not have.

Therefore the combined probability of aircraft being discovered without emergency locator is = 0.74*0.38 = 0.2812 = 28.12%

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