Question
Let X be a random variable following binomial distribution whose mean and variance are 200 and 160 respectively. What is the value of the number of trials (n)?
NDA
Mathematics
Probability
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. 500
- B. 1000
- C. 1500
- D. 2000
Answer
B. 1000
Step-by-step solution
Let n be the number of trials, p be the probability of success, and q be the probability of failure. Given mean = np = 200 Given variance = npq = 160 Dividing variance by mean: npq np = 160 200 q = 4 5 Since p + q = 1, we have p = 1 - 4 5 = 1 5 Substituting the value of p in the mean equation: n 1 5 = 200 n = 1000
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