A and B are two mutually exclusive events is given to us.
P (A) = 0.4 and P (B) = 0.5
By definition of mutually exclusive events we can write,
P (A ∪ B) = P (A) + P (B)
(i) P (A ∪ B) = P (A) + P (B) = 0.5 + 0.4 = 0.9
(ii) P (A′ ∩ B′) = P (A ∪ B)′ {using De Morgan’s Law}
P (A′ ∩ B′) = 1 – P (A ∪ B)
= 1 – 0.9
= 0.1