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AP EAMCET · Maths · Probability

If \(\mathrm{X} \sim \mathrm{B}(9, \mathrm{p})\) is a binomial variate satisfying the equation \(\mathrm{P}(\mathrm{x}=3)=\mathrm{P}(\mathrm{x}=6)\), then \(\mathrm{P}(\mathrm{x} < 3)=\)

  1. A \(\frac{23}{256}\)
  2. B \(\frac{65}{256}\)
  3. C \(\frac{5}{256}\)
  4. D \(\frac{45}{256}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{23}{256}\)

Step-by-step Solution

Detailed explanation

\(\binom{9}{3} p^3 (1-p)^6 = \binom{9}{6} p^6 (1-p)^3\) \((1-p)^3 = p^3\) \(1-p = p \Rightarrow p = 1/2\) \(P(x \(P(x \(P(x \(P(x < 3) = 46 / 512 = 23 / 256\)