A and B are events such that P(A)= 0.4, P(B)=0.3 and P(A ∪ B)= 0.5, then P(B ∩ A') is equal to :
Answer & explanation
Correct answer: option 2
The correct answer is option (2) → 0.1
$P(B ∩ A')=P(B)-P(A ∩ B)$ ...(1)
we know that
$P(A∪B)+P(A ∩ B)=P(A)+P(B)$
$P(A ∩ B)=P(A)+P(B)-P(A∪B)$
$=0.4+0.3-0.0.2=P(A ∩ B)$
so from (1) $P(B ∩ A')=0.3-0.2=0.1$