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

1.	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» (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.

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»

(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.

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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.

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