Question

If p(a)=0.2, p(b)=0.2, and a and b are mutually exclusive, are they independent?

Answer 1

he events are not independent

How to determine if they are mutually exclusive?

The given parameters are:

P(A) = 0.2

P(B) = 0.2

The events are mutually exclusive.

So, as have

P(A or B) = P(A) + P(B)

If the events are independent, then

P(A and B) = P(A) + P(B) - P(A or B)

P(A and B) = P(A) * P(B)

So, we have

P(A and B) = 0.2 + 0.2 - 0.2 - 0.2 = 0

P(A and B) = 0.2 * 0.2 = 0.04

The above equations are not equal

Hence, the events are not independent

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