Seventy 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 90% of the aircraft not discovered do not have such a locator. Suppose a light aircraft has disappeared. 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 : Step 1 : Given Seventy 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 90% of the aircraft not discovered do not have such a locator. Suppose a light aircraft has disappeared. a). 60% of 70% are discovered and have a locator.This is 42% of all aircraft that disappear. 40% of 70% are discovered and do not have a locator. This is 28% of all aircraft that disappear. 10% of 30% are not discovered but do have a locator. This is 3% of all aircraft that disappear. 90% of 30% are not discovered and do not have a locator. This is 27% of all aircraft that disappear. The table is given below. Locator Has Hasn't Total Discovered 42 28 70 Not discovered 3 27 30 Total 45 55 The numbers were filled as follows: I assumed the total number of light aircraft disappeared to be 100 70% of them (70) are discovered. So 30 are not discovered. 60% of the 70 discovered aircraft (42) have a locator. So 28 don't have it. 90% of those not located have not a locator (27) so 3 have one. The totals on the last line are just that. Let the probability that it will not be discovered. Total number of aircraft that do have a locator : 42 + 3 = 45 Number of aircraft that do have a locator but are not discovered, divided by total number of aircraft that have a locator : 3 45 45 have an emergency locator and 3 of them are not discovered, so the probability is 3/45 = 1/15 Therefore the probability that it will not be discovered is 1/15 .