# In each of Exercises the events A1, A2, . . . are mutually exclusive and exhaustive. We have provided P(A1), P(A2), . . . and P(B| A1), P(B| A2), . . . . In each case,a.use the rule of total probability to nd P(B).b.apply Bayes’s rule to nd P(A1| B).JP(Aj)P(B|Aj)10.40.820.60.7

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In each of Exercises the events A1, A2, . . . are mutually exclusive and exhaustive. We have provided P(A1), P(A2), . . . and P(B| A1), P(B| A2), . . . . In each case,

a.use the rule of total probability to nd P(B).
b.apply Bayes’s rule to nd P(A1| B).

 J P(Aj) P(B|Aj) 1 0.4 0.8 2 0.6 0.7
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Step 1

From the Bayes’ theorem, the conditional probability is given as follows.

Step 2

The value of P(B) can be calcu...

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