Question

Let E₁ and E₂ be the events such that P (E₁) = 1/3 and P (E₂) = 3/5.

Find:

(i) P (E₁ U E₂), when E₁ and E₂ are mutually exclusive,

(ii) P (E₁ ∩ E₂), when E₁ and E₂ are independent.

Answer 1

(i) P (E₁ U E₂), when E₁ and E₂ are mutually exclusive

We know that when two events are mutually exclusive

P (E₁ ∩ E₂) = 0

So P (E₁ U E₂) = P (E₁) + P (E₂)

By substituting the values

= 1/3 + 3/5

= 14/15

Hence, P (E₁ U E₂) = 14/15, when E₁ and E₂ are mutually exclusive.

(ii) P (E₁ ∩ E₂), when E₁ and E₂ are independent

We know that when two events are independent

P (E₁ ∩ E₂) = P (E₁) × P (E₂)

By substituting the values

= 1/3 × 3/5

= 1/5

Hence, P (E₁ ∩ E₂) = 1/5 when E₁ and E₂ are independent.