Question

If A, B and C are independent events, P(A ∩ B) = 1/2, P(B ∩ C) = 1/3, P(C ∩ A) = 1/6, then find P(A), P(B) and P(C).

Answer 1

Since A and B are independent events, 

P(A ∩ B) = P(A) . P(B) 

∴ P(A) . P(B) = 1/2……(i)

B and C are independent events.

∴ P(B ∩ C) = P(B) . P(C) 

∴ P(B) . P(C) = 1/3……(ii)

A and C are independent events. 

∴ P(A ∩ C) = P(A) . P(C)

∴ P(A) . P(C) = 1/6 ……(iii)

Dividing (i) by (ii), we get

Substituting P(C) = 1/3 in equation (ii), we get P(B) = 1

Substituting P(B) = 1 in equation (i), we get P(A) = 1/2