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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,

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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. Select the correct answer from above options

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(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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