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Let A and B be events in a sample space S. If it is known that Pr[A] = 0.4, Pr[B] = 0.2, and Pr[AB] =

Let A and B be events in a sample space S. If it is known that Pr[A] = 0.4, Pr[B] = 0.2, and Pr[AB] = 0.1, which of the following statements is/are true? Justify your answer.

(i) A and B are independent events

(ii) A and B are mutually exclusive events

(iii) Pr[B|A] = 0.5 (iv) Pr[Bc|A] = 0.75

(v) Pr[Ac|B] = 0.5

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