Question -
Answer -
(i) P(A) = 0.5, P(B) = 0.7, P(A ∩ B) = 0.6
P(A ∩ B) > P(A)
Therefore, the given probabilities are not consistentlydefined.
(ii) P(A) = 0.5, P(B) = 0.4, P(A ∪ B) = 0.8
Then,
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
0.8 = 0.5 + 0.4 – P(A ∩ B)
Transposing – P(A ∩ B) to LHS and it becomes P(A ∩ B) and0.8 to RHS and it becomes – 0.8.
P(A ∩ B) = 0.9 – 0.8
= 0.1
Therefore, P(A ∩ B) < P(A) and P(A ∩ B) < P(B)
So, the given probabilities are consistently defined.