Question

4 0/10 points multiple choice which condition is necessary for the multiplication rule to apply? events a and b must be independent event a must occur first event b must occur first events a and b must be mutually exclusive

Explanation:

To determine the necessary condition for the multiplication rule, we analyze each option:

• For the multiplication rule of probability (specifically for independent events), the formula is \( P(A \cap B) = P(A) \times P(B) \), which requires events \( A \) and \( B \) to be independent.
• The order of occurrence (whether \( A \) or \( B \) occurs first) is not a requirement for the multiplication rule.
• Mutually exclusive events have \( P(A \cap B) = 0 \), and the multiplication rule for independent events does not apply to mutually exclusive events (unless one of the events has probability 0).

So the correct condition is that events \( A \) and \( B \) must be independent.

Answer:

A. Events A and B must be independent