Financial Risk Manager Part 1

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Explanation:

Let's go step by step.

Step 1: Define events

Let:

Given:

P(D) = 0.25

P(\neg D) = 0.75

Correct positive diagnosis means test is positive given the person has the disease. So:

P(T^+ | D) = 0.95

Correct negative diagnosis means test is negative given the person does not have the disease. So:

P(T^- | \neg D) = 0.99

That means:

P(T^+ | \neg D) = 1 - 0.99 = 0.01

Step 2: Apply Bayes’ theorem

We want $P(D | T^+)$ :

P(D | T^+) = \frac{P(T^+ | D) \cdot P(D)}{P(T^+ | D) P(D) + P(T^+ | \neg D) P(\neg D)}

Substitute:

P(D | T^+) = \frac{0.95 \times 0.25}{0.95 \times 0.25 + 0.01 \times 0.75}

= \frac{0.2375}{0.2375 + 0.0075}

= \frac{0.2375}{0.2450}

\approx 0.969387...

Step 3: Interpret result

The probability that a person has the disease given a positive test is about 96.94%.

\boxed{0.969}

Explanation:

Let's go step by step.

Step 1: Define events

Let:

Given:

P(D) = 0.25

P(\neg D) = 0.75

Correct positive diagnosis means test is positive given the person has the disease. So:

P(T^+ | D) = 0.95

Correct negative diagnosis means test is negative given the person does not have the disease. So:

P(T^- | \neg D) = 0.99

That means:

P(T^+ | \neg D) = 1 - 0.99 = 0.01

Step 2: Apply Bayes’ theorem

We want $P(D | T^+)$ :

P(D | T^+) = \frac{P(T^+ | D) \cdot P(D)}{P(T^+ | D) P(D) + P(T^+ | \neg D) P(\neg D)}

Substitute:

P(D | T^+) = \frac{0.95 \times 0.25}{0.95 \times 0.25 + 0.01 \times 0.75}

= \frac{0.2375}{0.2375 + 0.0075}

= \frac{0.2375}{0.2450}

\approx 0.969387...

Step 3: Interpret result

The probability that a person has the disease given a positive test is about 96.94%.

\boxed{0.969}

Comments (1)

Yash ParwaniApr 11, 2026 8:48 AM

The option selected is incorrect. The correct answer is 0.96939

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TTanishq

Last updated: May 2, 2026 at 15:32

0.275

14.3%

0.15

14.3%

0.245

28.6%

0.97

28.6%