Question

If E₁ and E₂ are the two events such that P (E₁) = 1/4, P (E₂) = 1/3 and P (E₁ U E₂) = 1/2, show that E₁ and E₂ are independent events.

Answer 1

It is given that E₁ and E₂ are the two events such that P (E₁) = 1/4, P (E₂) = 1/3 and P (E₁ U E₂) = 1/2

We know that

P (E₁ ∩ E₂) = P (E₁) + P (E₂) – P (E₁ U E₂)

By substituting the values

= 1/4 + 1/3 – 1/2

= 1/12 …….. (1)

Condition: Two events are independent

P (E₁ ∩ E₂) = P (E₁) × P (E₂)

By substituting the values

= 1/4 × 1/3

= 1/12 ……. (2)

Here both the equations are same

So E₁ and E₂ are independent events

Therefore, it is proved.