Question

Let A and B be two events such that $P\left(\overline{A\cup B}\right)=\frac{1}{6},P(A\cap B)=\frac{1}{4}$ and $P\left(\overline{A}\right)=\frac{1}{4}$, where $\overline{A}$ stands for the complement of the event A. Then the events A and B are?

• A. Independent but not equally likely
• B. Independent and equally likely
• C. Mutually exclusive and independent
• D. Equally likely but not independent

Answer 1

The correct option is A Independent but not equally likely

P(A')=1/4 so P(A)=3/4

P(AUB)'=1/6, P(AUB)=5/6

P(A∩B)=1/4

P(AUB)=P(A)+P(B)-P(A∩B)=3/4+P(B)-1/4

5/6=1/2+P(B)

P(B)=2/6=1/3

P(A)*P(B)=1/3*3/4=1/4=P(A∩B)

A and B are independent but not equally likely