60. Seventy percent of the light aircraft that disappear while in flight in a ce

Question

60. Seventy percent of the light aircraft that disappear while in flight in a certain country are subsequently discov- ered. 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 7- #60 (book) that it will not be discovered? If it does not have an emergency locator, what is the probability that it will be discovered? b.

Explanation / Answer

Ans:

Given that

P(discovered)=0.70

P(not discovered)=1-0.7=0.3

P(locator/discovered)=0.6

P(not locator/discovered)=1-0.6=0.4

P(not locator/not discovered)=0.9

P(locator/not discovered)=1-0.9=0.1

a)P(not discovered/locator)=P(locator/not discoverd)*P(not discovered)/P(locator)

first find:

P(locator)=P(locator/discoverd)*P(discoverd)+P(locator/not discoverd)*P(not discoverd)

=0.6*0.7+0.1*0.3

=0.42+0.03=0.45

P(not locator)=1-0.45=0.55

P(not discovered/locator)=(0.1*0.3)/0.45=0.03/0.45=0.0667

b)

P(discovered/not locator)=P(not locator/discovered)*P(discovered)/P(not locator)

=(0.4*0.7)/0.55=0.5091

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