If A and B are two independent events such that P A > 1 2 , P A ∩ B C = 3 25 and P A C ∩ B = 8 25 , then P A is equal to (where, A c and B c represent the complement of events A and B respectively)

Step-by-step solution

A , B are independent events P A ∩ B C = P A P B C = P A 1 - P B = 3 25 … 1 P A C ∩ B = P A C ⋅ P B = 1 - P A P B = 8 25 ... 2 From 1 and 2 , we get, P B - P A = 1 5 ... 3 From 1 and 3 P B - 1 5 1 - P B = 3 25 Let, P B = t ⇒ 6 5 t - 1 5 - t 2 = 3 25 ⇒ 30 t - 5 - 25 t 2 = 3 ⇒ 25 t 2 - 30 t + 8 = 0 ⇒ t = 2 5 , 4 5 P B = 2 5 ⇒ P A = 1 5 P B = 4 5 ⇒ P A = 3 5 ∵ P A > 1 2 ⇒ P A = 3 5