Which of the following statements is not true? A)An event A and its complement are always mutually exclusive. B)A set of events is said to be collectively exhaustive if it includes all the possible outcomes of an experiment. C)The probability of event A and event B occurring must be equal to 1. D)When the events within a set are both mutually exclusive and exhaustive,the sum of their probabilities is 1.0.

Question

Quizplus · Accepted Answer

The probability of event A and event B occurring does not necessarily have to be equal to 1, unless A and B are the only possible outcomes of an experiment (in which case, they would be collectively exhaustive). In general, the probability of A and B occurring is given by P(A and B) = P(A) * P(B | A), where P(B | A) is the conditional probability of B given that A has occurred. This product can be less than, equal to, or greater than 1, depending on the probabilities of A and B and their conditional dependence. Therefore, statement C is not always true.

Which of the Following Statements Is Not True