Question

If \(A\) and \(B\) are two events such that \[ P(A \cup B)=\frac{5}{6}, \qquad P(A \cap B)=\frac{1}{3}, \qquad P(B')=\frac{1}{2}, \] then the events \(A\) and \(B\) are:

• A. dependent
• B. mutually exclusive
• C. independent
• D. equally likely

Hint:

To test for independence, calculate the product \(P(A) \times P(B)\).
If it equals \(P(A \cap B)\), the events are independent.
If \(P(A \cap B) = 0\), the events are mutually exclusive.

Answer 1

The Correct Option is C