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

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, 66% have an emergency locator, whereas 86% of the aircraft not discovered do not 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

From the given data, the following Table is formed:

                                  Discovered          Not discovered               Total

Have Emergency Locator      0.75X0.65=0.4875        0.25X0.86=0.215             0.7025

No Emergency Locator         0.75X0.35=0.2625        0.25X0.14=0.035            0.2975

Total                                         0.75                            0.25                           1

(a) P(Have emergency locator & Not discovered) = 0.215

(b) P(No emergency locator & discovered) = 0.263

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