A and B are two events is given
P (A) = 0.54, P (B) = 0.69 and P (A ∩ B) = 0.35
By definition of P (A or B) under axiomatic approach we can write,
P (A ∪ B) = P (A) + P (B) – P (A ∩ B)
(i) P (A ∩ B′)
P (only A) = P (A) – P (A ∩ B)
∴ P (A ∩ B′) = P (A) – P (A ∩ B)
= 0.54 – 0.35
= 0.19
(ii) P (A′ ∩ B)
P (only B) = P (B) – P (A ∩ B)
∴ P (A′ ∩ B) = P (B) – P (A ∩ B)
= 0.69 – 0.35
= 0.34