5.3 Exercise 2 — Applied Probability

Suppose $\left\{A_{1} , A_{2} , A_{3}\right\} ci \left|\right. C$ and $ci \left|\right. C^{c}$ , with $P \left(C\right) = 0 . 4$ , and

P \left(\right. A_{i} \left|\right. C \left.\right) = 0 . 90 , 0 . 85 , 0 . 80 P \left(\right. A_{i} \left|\right. C^{c} \left.\right) = 0 . 20 , 0 . 15 , 0 . 20 \text{for} i = 1 , 2 , 3 , \text{respectively}

Determine the posterior odds $P \left(\right. C \left|\right. A_{1} A_{2}^{c} A_{3} \left.\right) / P \left(\right. C^{c} \left|\right. A_{1} A_{2}^{c} A_{3} \left.\right)$ .

Pfeiffer, Applied Probability, 5.3 Problems on Conditional Independence, exercise 2

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