Answer-first summary for fast verification
Answer: 0.79
This is a classic Bayes' theorem application. Let: - L = Event a project makes a loss - S = Event of a standard project - P₁ = Event of a preferred project - U = Event of an ultra-preferred project 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.
Author: Tanishq Prabhu
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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)?
A
0.79
B
0.73
C
0.22
D
0.15
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