If $\mathbf{A}$ and $\mathbf{B}$ are two events associated with a random experiment such that $\mathrm{P}$ $(\mathbf{A} \cup \mathbf{B})=\mathbf{0 . 8}, \mathbf{P}(\mathbf{A} \cap \mathbf{B})=\mathbf{0 . 3}$ and $\mathrm{P}(\overline{\mathrm{A}})=\mathbf{0 . 5}$, find $\mathrm{P}(\mathbf{B})$

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