There are three events A B and C as follows A 135 B 24 and C

There are three events A, B and C as follows; A ={1,3,5}, B= {2,4} and C= {2,5,6}. The probabilities of the sample points are P(1)=0.2, P(2)= 0.2, P(3) = 0.1, P(4)=0.2 , P(5)=0.1 and P(6)=0.2

1) are A and B independent ? Mutually exclusive?

2)Are B and C independet? Mutually exclusive?

Solution

A ={1,3,5}, B= {2,4} and C= {2,5,6}

P(1)=0.2, P(2)= 0.2, P(3) = 0.1, P(4)=0.2 , P(5)=0.1 and P(6)=0.2

As A and B do not have anything in common, A and B are mutually exclusive

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B and C have 2 in common. Hence not mutually exclusive

P(B) = 0.2+0.2=0.4

P(C) = 0.2+0.1+0.2 = 0.5

P(BC) = P(2) = 0.2 = 0.4(0.5)

= P(B) P(C)

Hence B and C are independent.