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Let A and B be the events such that P (A) = 1/2, P (B) = 7/12 and P (not A or not B) = 1/4. State whether A and B are

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Let A and B be the events such that P (A) = 1/2, P (B) = 7/12 and P (not A or not B) = 1/4. State whether A and B are (i) mutually exclusive, (ii) independent. Select the correct answer from above options

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(i) If A and B are mutually exclusive P (not A or not B) = 1/4 i.e. By substituting the values P (A ∩ B) = 1 – 1/4 = 3/4 …… (1) For two mutually exclusive events P (A ∩ B) = 0 but here P (A ∩ B) ≠ 0 Hence, A and B are not mutually exclusive. (ii) If A and B are independent Two events is independent is written as P (E1 ∩ E2) = P (E1) × P (E2) By substituting the values = 1/2 × 7/12 = 7/24 ……. (2) Here equation (1) is not equal to equation (2) Hence, A and B are not independent.

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