Financial Risk Manager Part 1

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Explanation:

Given: $P(H)=0.25,\; P(+)=0.20,\; P(+\mid H')=0.05.$

Find sensitivity from total probability:

0.20 = P(+\mid H)\cdot0.25 + 0.05\cdot0.75 \implies P(+\mid H)=0.65.

So $P(-\mid H)=0.35,\; P(-\mid H')=0.95.$

Compute $P(-)$ :

P(-)=0.35\cdot0.25+0.95\cdot0.75=0.80.

Apply Bayes for $P(H'\mid -)$ :

P(H'\mid -)=\frac{P(-\mid H')P(H')}{P(-)}=\frac{0.95\cdot0.75}{0.80}=\frac{0.7125}{0.80}\approx0.890625\;(89.06\%).

Conclusion: the correct posterior ≈89.1%. None of the given choices match exactly; C (87%) is closest and D (93%) is incorrect.

Explanation:

Given: $P(H)=0.25,\; P(+)=0.20,\; P(+\mid H')=0.05.$

Find sensitivity from total probability:

0.20 = P(+\mid H)\cdot0.25 + 0.05\cdot0.75 \implies P(+\mid H)=0.65.

So $P(-\mid H)=0.35,\; P(-\mid H')=0.95.$

Compute $P(-)$ :

P(-)=0.35\cdot0.25+0.95\cdot0.75=0.80.

Apply Bayes for $P(H'\mid -)$ :

P(H'\mid -)=\frac{P(-\mid H')P(H')}{P(-)}=\frac{0.95\cdot0.75}{0.80}=\frac{0.7125}{0.80}\approx0.890625\;(89.06\%).

Conclusion: the correct posterior ≈89.1%. None of the given choices match exactly; C (87%) is closest and D (93%) is incorrect.

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NNikitesh

Last updated: February 12, 2026 at 11:49

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70%

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87%

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93%

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