Question

Let \(E\) and \(F\) be two events such that \[ P(\bar E)=\frac13,\qquad P(E\cap F)=\frac13,\qquad P(\overline{E\cup F})=\frac16. \] Which of the following is correct?

• A. \(E\) and \(F\) are not equally likely but independent
• B. \(E\) and \(F\) are mutually exclusive and independent
• C. \(E\) and \(F\) are equally likely but not independent
• D. \(E\) and \(F\) are independent and equally likely

Hint:

To check independence, verify \[ \boxed{P(E\cap F)=P(E)P(F).} \] To check whether two events are equally likely, compare \[ \boxed{P(E)\ \text{and}\ P(F).} \]

Answer 1

The Correct Option is A