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Suppose that A, B and C are events in a sample space S, such that:
• A and B are equally likely;
• C is four times as likely as B;
• B and C are independent;
• if either B or C occurs, then A cannot occur;
• at least one of A, B or C must occur.
(i) Write the above statements as formal statements about the events A, B and C, either in terms of probabilities.
(ii) Hence derive P(A), P(B) and P(C).
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