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P( A ∩ B ) = 0.12 ,    P( Ac∩ B ) = 0.18 ,   and...

P( A ∩ B ) = 0.12 ,    P( Ac∩ B ) = 0.18 ,   and A & B are independent events.

      What is   P( Ac ∪ B ) ?

Math   Statistics-And-Probability   
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Answer #1

We are given here that:
P( A ∩ B ) = 0.12 which means that P(A and B) = 0.12

Also, we are given here that:
P( Ac∩ B ) = 0.18, which means that P( not A and B) = 0.18

Therefore, P(B) = P( A ∩ B ) + P( Ac∩ B ) = 0.18 + 0.12 = 0.3.

As A and B are independent events, therefore,
P(A) = P( A ∩ B ) / P(B) = 0.12 / 0.3 = 0.4

P(Ac) = 1 - P(A) = 1 - 0.4 = 0.6

Using law of addition of probability, we have here:
P(Ac   ∪ B) = P(Ac) + P(B) - P( Ac∩ B ) = 0.6 + 0.3 - 0.18 = 0.72

Therefore 0.72 is the required probability here.

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