(Step-by-Step) Here we look at some variations of Example 1.3.4. In the warden's calculation of Example 1.3.4 it was assumed that if A were to be pardoned,

Question: Here we look at some variations of Example 1.3.4.

In the warden's calculation of Example 1.3.4 it was assumed that if A were to be pardoned, then with equal probability the warden would tell A that either $\mathrm{B}$ or $\mathrm{C}$ would die. However, this need not be the case. The warden can assign probabilities $\gamma$ and $1-\gamma.$ to these events, as shown here:

Calculate $P(A \mid \mathcal{W})$ as a function of $\gamma .$ For what values of $\gamma$ is $P(A \mid \mathcal{W})$ less than, equal to, or greater than $\frac{1}{3} ?$

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(Step-by-Step) Here we look at some variations of Example 1.3.4. In the warden's calculation of Example 1.3.4 it was assumed that if A were to be pardoned,

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