If A and B are two independent events such that , then write the values of P(A) and P(B).

Question

Philoid · Accepted Answer

As A and B are independent events.

∴ P(A ∩ B) = P(A)P(B) = 1/6

Also, P(A’ ∩ B’) = P(A’)P(B’) = 1/3

⇒ (1 – P(A))(1 – P(B)) = 1/3

⇒ 1 + P(A)P(B) – P(A) – P(B) = 1/3

⇒ 1 + 1/6 – 1/3 = P(A) + P(B)

⇒ 1 – 1/6 = P(A) + P(B)

∴ P(A) = 5/6 – P(B)

Let P(B) = x

∴ (5/6 – x)x = 1/6

⇒ 5x – 6x² = 1

⇒ 6x² – 5x + 1 = 0

⇒ 6x² – 3x – 2x + 1 = 0

⇒ 3x(2x – 1) – (2x – 1) = 0

⇒ (3x – 1)(2x – 1)=0

∴ x = 1/3 or x = 1/2

∴ P(B) = 1/3 or 1/2

∴ P(A) = 1/2 or 1/3