Question 1

Scenario: Suppose a light aircraft has disappeared.

Events:

  • - Has been discovered after disappearing.
  • - Has an emergency locator.

Probabilities:

  • .
  • .
  • .
  • .

(a)

Problem: If it has an emergency locator, what is the probability that it will not be discovered?

Process: The question can be rephrased to ask what the probability is of a plane not being discovered after disappearing given that it has an emergency locator. This would be the conditional probability . We can use Bayes' Theorem. We have to find the probability using the law of total probability.

Answer: 0.065.

Summary

To find if you're given :
To find the probability if the sample space is partitioned by mutually exclusive and exhaustive events :
To find the probability if the sample space is partitioned by and :

  • - First partition of the sample space.
  • - Second partition of the sample space.

(b)

Problem: If it does not have an emergency locator, what is the probability that it will be discovered?

Process: The question can be rephrased to ask what the probability is of a plane being discovered given that it doesn't have an emergency locator. This would be the conditional probability . Since we now know and , we can use Bayes' Theorem.

Answer: 0.491.

Summary

To find if you're given :