According to the following table of joint probabilities,
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(a) Determine P(A1|B1).
(b) Determine P(A2|B1).
(c) Do the answers to parts (a) and (b) sum to 1? Is this a coincidence?
(d) Determine P(A1|B2)
(e) Determine P(B2|A1)
(f) Did you expect the answers to parts (a) and (b) to be reciprocals? Why is this impossible (unless all probabilities are 1)?
(g) Are events A and B independent?