Financial Risk Manager Part 1

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Explanation:

Let:
D = Event of death
VT = Event of vegetarians
OM = Event of omnivores
VG = Event of vegan

We need to calculate P(OM | D)

Now, we already know that:
P(D | VT) = 2P(D | VG) and P(D | VT) = $\frac{1}{2}$ P(D | OM)

Applying Bayes’ theorem,

P(\text{OM} \mid D) = \frac{P(\text{OM}) \times P(D \mid \text{OM})}{(P(\text{OM}) \times P(D \mid \text{OM}) + P(\text{VT}) \times P(D \mid \text{VT}) + P(\text{VG}) \times P(D \mid \text{VG}))}

= \frac{2P(D \mid VT) \times 0.75}{(2P(D \mid VT) \times 0.75) + P(D \mid VT) \times 0.15 + \frac{1}{2}P(D \mid VT) \times 0.10}

= \frac{1.5}{1.5 + 0.15 + 0.05}

= 0.8823

Explanation:

Let:
D = Event of death
VT = Event of vegetarians
OM = Event of omnivores
VG = Event of vegan

We need to calculate P(OM | D)

Now, we already know that:
P(D | VT) = 2P(D | VG) and P(D | VT) = $\frac{1}{2}$ P(D | OM)

Applying Bayes’ theorem,

P(\text{OM} \mid D) = \frac{P(\text{OM}) \times P(D \mid \text{OM})}{(P(\text{OM}) \times P(D \mid \text{OM}) + P(\text{VT}) \times P(D \mid \text{VT}) + P(\text{VG}) \times P(D \mid \text{VG}))}

= \frac{2P(D \mid VT) \times 0.75}{(2P(D \mid VT) \times 0.75) + P(D \mid VT) \times 0.15 + \frac{1}{2}P(D \mid VT) \times 0.10}

= \frac{1.5}{1.5 + 0.15 + 0.05}

= 0.8823

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Last updated: May 21, 2026 at 04:19

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