Given P(A ∪ B) = 0.7, P(A ∩ B)= 0.2 and P(B) = 0.5
To find P(A)
Now, P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
(i.e.,) 0.7 = P(A) + 0.5 – 0.2
⇒ 0.7 – 0.5 + 0.2 = P(A)
(i.e.,) P(A) = 0.4
Now P(A ∩ B) = 0.2 … (i)
P(A) P(B) = 0.4 × 0.5 = 0.2 … (ii)
(1) = (2) ⇒ P(A ∩ B) = P(A) P(B)
⇒ A and B are independent.