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7. [10 marks] A and B are two events in a sample space S with probabilities P [ A ] and P [ B ]
respectively. A) Find P [ A B ] under the following different circumstances: (a) A and B are
disjoint. (b) A is a subset of B . (c) B is a subset of A . (d) A and B are independent. B) Show
that if P [ A B ] > P [ A ] then P [ B A ] > P [ B ] and comment on whether in this case A and B
are independent.

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