A and B are two events is given
P (A) = 0.3, P (B) = 0.5 and P (A ∪ B) = 0.5
We need to find P (A ∩ B).
By definition of P (A or B) under axiomatic approach we know,
P (A ∪ B) = P (A) + P (B) – P (A ∩ B)
So, P (A ∩ B) = P (A) + P (B) – P (A ∪ B)
P (A ∩ B) = 0.3 + 0.4 – 0.5
= 0.7 – 0.5
= 0.2
∴ P (A ∩ B) is 0.2