problem 38

2.2.5 problem 38

Let $S$ be the event that an email is spam. Let $L = W_{1}^{c}, . . ., W_{22}^{c}, W_{23}, W_{24}^{c}, . . ., W_{64}^{c}, W_{64}, W_{65}, W_{66}^{c}, . . ., W_{100}^{c}$

Let $q = \prod_{j} (1 - p_{j})$ where $1 \leq j \leq 100 : j \notin 23, 64, 65$ .

Let $x = \prod_{j} (1 - r_{j})$ where $1 \leq j \leq 100 : j \notin 23, 64, 65$ .

P (S ∣ ∣ ∣ L) = \frac{P (S) P (L | S)}{P (L)} = \frac{p p_{23} p_{64} p_{65} q}{p p_{23} p_{64} p_{65} q + (1 - p) r_{23} r_{64} r_{65} x} .

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