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, 60% 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? 0.579 (b) If it does not have an emergency locator, what is the probability that it will be discovered? __________

Explanation / Answer

If light aircraft disappears then ,P ( light aircraft are discovered ) = 0.74 ,

P( light aircraft are not discovered ) = 1 - 0.74 = 0.26

P ( light aircraft are discovered and have emergency locator ) = 0.6

P ( light aircraft are not discovered and have emergency locator ) = 1- 0.6 = 0.4

P( light aircraft are not discovered and have don't have an emergency locator ) = 0.83

P( light aircraft are discovered and have don't have an emergency locator ) = 1 - 0.83 = 0.17

Now , if aircraft disappears ,

a) P ( it has emergency locator and it will not be discovered) = P (if disappear then light aircraft not discovered ) /

P ( light aircraft has emergency locator and not discovered)

= 0.26 / 0.4

= 0.650

b) P ( it does not have emergency locator and it is discovered ) =

P ( light aircraft does not have emergency locator and discovered ) /

P ( if disappear light aircraft discovered)

= 0.17 / 0.74

= 0.230

=

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