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Question

Let A and B be two events such that P(¯¯¯¯¯¯¯¯¯¯¯¯¯¯AB)=16,P(AB)=14 and P(¯¯¯¯A)=14, where ¯A stands for the complement of the event A. Then, the events A and B are ?


Correct Answer
A
Independent but not equally likely
Your Answer
B
Independent and equally likely
Your Answer
C
Mutually exclusive and independent
Your Answer
D
Equally likely but not independent

Solution

The correct option is A Independent but not equally likely
Given, P(¯¯¯¯¯¯¯¯¯¯¯¯¯¯AB)=16;P(AB)=14;P(¯A)=14
P(AB)=1P(¯¯¯¯¯¯¯¯¯¯¯¯¯¯AB)=116=56
And P(A)=1P(¯A)=114=34
P(AB)=P(A)+P(B)P(AB)
56=34+P(B)14
P(B)=13 A and B are not equally likely P(AB)=P(A).P(B)=14
So, events A and B are independent.
 

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