Quantitative Analysis for Management, 13/e

2.3 Further Probability Revisions

Although one revision of prior probabilities can provide useful posterior probability estimates, additional information can be gained from performing the experiment a second time. If it is financially worthwhile, a decision maker may even decide to make several more revisions.

Returning to the previous example, we now attempt to obtain further information about the posterior probabilities as to whether the die just rolled is fair or loaded. To do so, let us toss the die a second time. Again, we roll a 3. What are the further revised probabilities?

To answer this question, we proceed as before, with only one exception. The probabilities $P\left(\text{fair}\right)=0.50$ and $P\left(\text{loaded}\right)=0.50$ remain the same, but now we must compute ...