Question

If P(A)=0.25,P(B)=0.4andP(A∪B)=0.5findP(A∩B)andP(A∩ˉB)

Answer 1

Answer:

P( A ∩ B ) = 0.15

P( A ∩ ¬B ) = 0.1

Hello.  I hope this helps!

Step-by-step explanation:

P( A ∩ B ) = P( A ) + P( B ) - P( A ∪ B ) = 0.25 + 0.4 - 0.5 = 0.15

P( A ∩ ¬B ) = P( A ) - P( A ∩ B ) = 0.25 - 0.15 = 0.1

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Additional explanation, if needed:

P( A ∩ ¬B )  +  P( A ∩ B ) = P( (A ∩ ¬B) ∪ (A ∩ B) ) = P( A ∩ (¬B ∪ B ) ) = P( A )

=> P( A ∩ ¬B ) = P( A ) - P( A ∩ B ) = 0.25 - 0.15 = 0.1