question_answer

Let A and B be two events such that \[P\overline{(A\cup B)}=\frac{1}{6},P(A\cap B)=\frac{1}{4}\]and\[P(\overline{A})=\frac{1}{4},\]where \[\overline{A}\] stands for complement of event A. Then, events A and B are     AIEEE  Solved  Paper-2005

A) mutually exclusive and independent

B) independent but not equally likely

C) equally likely but not independent

D) equally likely and mutuaiiy exclusive

Correct Answer: B

Solution :

Given that.            and Clearly, So, the events A and B are independent events but not equally likely. Note Two events A and 3 are said to equally likely, ifand known as independent events, if.