Problem 4: Eighty percent of the light aircraft that disappear while in flight i

Question

Problem 4: Eighty percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, 70% have and emergency locator, whereas 80% of the aircraft not discovered do not have such a locator. Suppose a light aircraft has disappeared. a) What is the probability that it will be discovered and has an emergency locator? b) What is the probability that it will not be discovered and has an emergency locator? c) What is the probability that it has an emergency locator? d) If it has an emergency locator, then what is the probability that it will not be discovered? e) Do you think discovering an aircraft is statistically independent from having an emergency locator? Explain with numerical evidence.

Explanation / Answer

a)P(discovered and emegency locator)=P(discovered)*P(emergency locator|discovered)=0.8*0.7=0.56

b)

P(not discovered and emerency locator)=P(not discovered)*P(emergency locator|not discovered)=0.2*0.2=0.04

c)

P(emergency locator)=P(discovered and emegency locator)+P(not discovered and emerency locator)

=0.56+0.04=0.60

d)

P(not discovered|emergency locator)=P(not discovered and emerency locator)/P(emergency locator)

=0.04/0.60=0.0667

e)

as P(not discovered|emergency locator) is not equal to P(not discovered); therefore discovering an aircraft is not statistically independent from having an emergency locator.

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