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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.

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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. Select the correct answer from above options

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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.

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