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AP EAMCET202421 May 2024Evening ShiftMathematicsProbabilityActual

If X B(5, p) is a binomial variate such that p(X=3)=p(X=4) , then p(|X-3| 2)=

Options

  1. A242 243
  2. B201 243
  3. C200 243
  4. D121 243

Correct answer

C. 200 243

Step-by-step solution

aligned & X B(5, p) & p(X=3)=p(X=4) & ^5 C₃ p^3(1-p)^2= ^5 C₄ p^4(1-p) & 10(1-p)=5 p p= 10 15 = 2 3 & p(|X-3| 2)=p(-2 X-3 2)=p(1 X 5) & =p(X=2)+p(X=3)+p(X=4)=p(X=2)+2 p(X=3) & = ^5 C₂ ( 2 3 )^2 ( 1 3 )^3+2^5 C₃ ( 2 3 )^3 ( 1 3 )^2= 200 243 . aligned

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