Question
In a sample survey of a village, the probability that a farmer is in debt is 0.60. What is the probability that three randomly selected farmers are all in debt (assume independence of events)?
NDA
Mathematics
Probability
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. 0.000216
- B. 0.064
- C. 0.216
- D. 0.512
Answer
C. 0.216
Step-by-step solution
Let P(D) be the probability that a farmer is in debt. P(D) = 0.60 Since the selection of farmers is independent, the probability that all three randomly selected farmers are in debt is given by: P(D_1 D_2 D_3) = P(D_1) P(D_2) P(D_3) = 0.60 0.60 0.60 = 0.216 Answer: 0.216
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