Question

If A and B are two independent events such that P(A ∪ B) = 0.6, P(A) = 0.2, find P(B).

Answer 1

Given A and B are independent. 

⇒ P(A ∪ B) = P(A).P(B) 

Here P(A ∪ B) = 0.6 and P(A) = 0.2 

To find P(B): 

Now, P(A ∪ B) = P(A) + P(B) – P(A ∩ B) 

(i.e.,) P(A ∪ B) = P(A) + P(B) – P(A) . P(B) 

(i.e.,) 0.6 = 0.2 + P(B) (1 – 0.2)

P(B) (0.8) = 0.4 

⇒ P(B) = 0.4/0.8 = 4/8 = 1/2 = 0.5.