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?