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BITSAT2015MathematicsProbabilityActual

If in a binomial distribution n =4, P ( X =0)= 16 81 , then P ( X =4) equals

Options

  1. A1 16
  2. B1 81
  3. C1 27
  4. D1 8

Correct answer

B. 1 81

Step-by-step solution

Given n=4 and P(X=0)= 16 81 Let p be the probability of success and q that of failure in a trial. Then, P ( X =0)= ⁴ C ₀ p ⁰ q ⁴= 16 81 q ⁴= ( 2 3 )⁴ ( n 0 =1 ) q = 2 3 p = 1 3 P ( X =4)= ⁴ C ₄ p ⁴ q ⁰= p ⁴= ( 1 3 )⁴= 1 81

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