I write the above statements as formal statements about the

Question

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).