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