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, 70% have an emergency locator, whereas 89% 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

Answer 1

0.05 = 5% probability that it will not be discovered

Explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Has an emergency locator

Event B: Not discovered

Probability of having an emergency locator:

70% of 75%(discovered).

100 - 89 = 11% of 100 - 75 = 25%(not discovered). So

`P(A) = 0.7*0.75 + 0.11*0.25 = 0.5525`

Intersection of events A and B

Having an emergency locator and not discovered, so 11% of 25%

`P(A \cap B) = 0.11*0.25 = 0.0275`

What is the probability that it will not be discovered?

`P(B|A) = (P(A \cap B))/(P(A)) = (0.0275)/(0.5525) = 0.05`

0.05 = 5% probability that it will not be discovered