A and B are two events is given
P (A′) = 0.5, P (A ∩ B) = 0.3 and P (A ∪ B) = 0.8
Since, P (A′) = 1 – P (A)
P (A) = 1 – 0.5
= 0.5
We need to find P (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 (B) = P (A ∪ B) + P (A ∩ B) – P (A)
P (B) = 0.8 + 0.3 – 0.5
= 1.1 – 0.5
= 0.6
∴ P (B) is 0.6