Do all of the exercises in a Bayes’ theorem table. Do in addition try out at least one by using the formula directly, to see for yourself that the two methods give the same result.

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i. Calculate P(B). ii. Calculate all posterior probabilities P(A|B). (a) Prior: P(A) = P(A2)= Likelihood: P(BIA) = 0.7, P(B|A2) = 0.3 (b) Prior: P(A) = P(A) = Likelihood: P(BIA) = 0.07, P(B|A) = 0.03 (c) Prior: P(A) = P(A2) = P(A3)= Likelihood: P(BIA) = 0.12, P(B|A2) = 0.87, P(B|A3) = 0.01 (d) Prior: P(A) = P(A) = P(A3)= Likelihood: P(BIA) = 0.0012, P(B|A2) = 0.0087, P(B|A3)= 0.0001 (e) Prior: P(A) = 0.3, P(A2) = 0.7 Likelihood: P(B|A) = 0.001, P(B|A) = 0.011 (f) Prior: P(A)=0.1, P(A2) = 0.9 Likelihood: P(BIA) = P(B|A) = (g) Prior: P(A) = P(A2) = P(A3)= Likelihood: P(BA) = 0.012, P(B|A2)=0.001, P(B|A3) = 0.7 (h) Prior: P(A)=0.237 1, P(A2) = 0.4554, P(A3) = 0.3075 Likelihood: P(B|A) = 0.8, P(B|A2) = 0.07, P(B|A3) = 0.2 (1) Prior: P(A)=0.07, P(A2) = 0.07, P(A3) = 0.07, P(A4) = 0.79 Likelihood: P(B|A) = 0.8, P(B|A2) = 0.07, P(B|A3)=0.007, P(BA) 0.0007