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NDA 2025
Exam
NDA
Year
2025
Subject
Mathematics
Chapter
Probability

NDA 2025 · Mathematics · Probability

In a sample survey of a village, the probability that a farmer is...

In a sample survey of a village, the probability that a farmer is in debt is 0.600.60. What is the probability that three randomly selected farmers are all in debt (assume independence of events)?

Options

  1. A0.0002160.000216
  2. B0.0640.064
  3. C0.2160.216
  4. D0.5120.512

Correct answer

C. 0.2160.216

Step-by-step solution

Let P(D)P(D) be the probability that a farmer is in debt.

P(D)=0.60P(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(D1∩D2∩D3)=P(D1)×P(D2)×P(D3)P(D_1 \cap D_2 \cap D_3) = P(D_1) \times P(D_2) \times P(D_3)

=0.60×0.60×0.60= 0.60 \times 0.60 \times 0.60

=0.216= 0.216

Answer: 0.2160.216
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