Given: A and B are two mutually exclusive events.
P (A) = 0.4 and P (B) = 0.5
By definition of mutually exclusive events we know that:
P (A ∪ B) = P (A) + P (B)
Now, we have to find
(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
(iii) P (A′ ∩ B) [This indicates only the part which is common with B and not A.
Hence this indicates only 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
(iv) P (A ∩ B′) [This indicates only the part which is common with A and not B.
Hence this indicates only A]
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
