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KCET2024MathematicsProbability

If a random variable X follows the binomial distribution with parameters n=5, p and P(X=2)=9 P(X=3) , then p is equal to

Options

  1. A10
  2. B1 / 10
  3. C5
  4. D1 / 5

Correct answer

B. 1 / 10

Step-by-step solution

p(X=2)=9 p(X=3) (where, n=5 and q=1-p) ^5 C₂ p^2(1-p)^3=9 ^5 C₃ p^3(1-p)^2 5! 2!3! p^2(1-p)^3=9 5! 3!2! p^3(1-p)^2 p^2(1-p)^3 p^3(1-p)^2 =9 1-p p =9 9 p+p=1 10 p=1 p= 1 10

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