Question

A and B are two events. P(A)=0.45, P(B)=0.2, P(A & B) =0.65

Are the two events independent?
Use the concept of conditional probability to support your answer.

Answer 1

Answer: No, the events are not independent

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Step-by-step explanation

If P(A & B) = P(A)*P(B) is a true equation, then events A and B are independent.

So,

P(A)*P(B) = 0.45*0.2 = 0.09

which does not match with P(A & B) =0.65

Therefore, P(A & B) = P(A)*P(B) is false and we conclude the two events are not independent. They are dependent. A depends on B, or vice versa.