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NDA 2026 · PYQ · Probability / Binomial Distribution · medium

For a Binomial distribution with mean 6 and standard deviation √2, what is the value of P(X = 0)?

  1. A.(1/3)⁹✓ Correct
  2. B.(2/3)⁹
  3. C.(1/3)(2/3)⁸
  4. D.(2/3)(1/3)⁸

Explanation

For a binomial distribution, mean = np = 6 and variance = npq = 2. So q = npq/np = 2/6 = 1/3, which gives p = 2/3. Then n = 6/p = 6/(2/3) = 9. P(X = 0) = q^n = (1/3)^9.
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