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JEE Main202226 Jul 2022Morning ShiftMathematicsProbabilityActual

The mean and variance of a binomial distribution are α and α 3 respectively. If P X = 1 = 4 243 , then P X = 4 or 5 is equal to:

Options

  1. A5 9
  2. B64 81
  3. C16 27
  4. D145 243

Correct answer

C. 16 27

Step-by-step solution

Given mean n p = α           ⋯ 1 Also given variance n p q = α 3         ⋯ 2 From 1 and 2 q = 1 3 and p = 2 3 Now P X = 1 = 4 243 ⇒ C 1 n q n - 1 p 1 = 4 243 ⇒ n 3 n = 2 243 ⇒ n = 6 So, P 4   or   5 = C 4 6 2 3 4 1 3 2 + C 5 6 2 3 5 · 1 3 0 = 16 27

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