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 (only B) = P (B) – P (A ∩ B)
As A and B are mutually exclusive so they don’t have any common parts.
P (A ∩ B) = 0
∴ P (A′ ∩ B) = P (B) = 0.5
(ii) P (A ∩ B′)
P (only A) = P (A) – P (A ∩ B)
As A and B are mutually exclusive so they don’t have any common parts.
P (A ∩ B) = 0
∴ P (A ∩ B′) = P (A) = 0.4