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).

I am having trouble expressing the statements in terms of probability and how would you find these probabilities from the information given?