An investment firm classifies capital projects into three different categories, depending on risk level: Standard, Preferred, and Ultra-preferred. Of the firm's projects, 60% are standard, 30% are preferred, and 10% are ultra-preferred. The probabilities of a project making a loss are 0.01, 0.005, and 0.001 for categories standard, preferred, and ultra-preferred respectively. If a capital project makes a loss in the next year, then what is the probability that the project was standard (correct to 2 decimal places)?

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Explanation:

This is a classic Bayes' theorem application. Let:

We need to find P(S|L):

$P(S | L) = \frac{P(S) \times P(L|S)}{P(S) \times P(L|S) + P(P_1) \times P(L|P_1) + P(U) \times P(L|U)}$

$= \frac{(0.6 \times 0.01)}{(0.6 \times 0.01) + (0.3 \times 0.005) + (0.1 \times 0.001)}$

$= \frac{0.006}{0.006 + 0.0015 + 0.0001}$

$= \frac{0.006}{0.0076} = 0.7895 \text{ or } 79\%$

Rounded to 2 decimal places, this gives 0.79, which matches option A.

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Financial Risk Manager Part 1