Question 4.49

4.49 What's wrong?

In each of the following scenarios, there is something wrong. Describe what is wrong and give a reason for your answer.

  1. If two events are disjoint, we can multiply their probabilities to determine the probability that they will both occur.
  2. If the probability of is 0.6 and the probability of is 0.5, the probability of both and happening is 1.1.
  3. If the probability of is 0.35, then the probability of the complement of is −0.35.

4.49

(a) The statement is corrected by replacing disjoint with independent. Disjoint events cannot both occur. (b) A probability can never be bigger than 1. Also, the probability of both and happening is (0.6)(0.5) if and are independent. (c) A probability can never be negative. The probability of the complement of is 1 minus the probability of or