Given A and B are two mutually exclusive events

And, P(A) = 0.35 P(B) = 0.45

By definition of mutually exclusive events we know that:

P(A ∪ B) = P(A) + P(B)

We have to find-

i) P(A ∪ B) = P(A) + P(B) = 0.35 + 0.45 = 0.8

ii) P(A ∩ B) = 0 {∵ nothing is common between A and B}

iii) P(A ∩ B’) = This indicates only the part which is common with A and not B ⇒ 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) = 0.35

iv) P(A’ ∩ B’) = P(A ∪ B)’ {using De Morgan’s Law}

⇒ P(A’ ∩ B’) = 1 – P(A ∪ B) = 1 – 0.8 = 0.2