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AP EAMCET · Maths · Probability

If X is a binomial variate with mean \(\frac{16}{5}\) and variance \(\frac{48}{25}\), then \(\mathrm{P}(\mathrm{X} \leq 2)=\)

  1. A \(\frac{3^6(169)}{5^8}\)
  2. B \(\frac{3^7(71)}{5^8}\)
  3. C \(\frac{3^8}{(43) 5^8}\)
  4. D \(\frac{3^6(158)}{5^8}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{3^6(169)}{5^8}\)

Step-by-step Solution

Detailed explanation

\(q = \frac{npq}{np} = \frac{48/25}{16/5} = \frac{3}{5}\) \(p = 1 - q = 1 - \frac{3}{5} = \frac{2}{5}\) \(n = \frac{np}{p} = \frac{16/5}{2/5} = 8\) \(\mathrm{P}(\mathrm{X} \leq 2) = \mathrm{P}(\mathrm{X}=0) + \mathrm{P}(\mathrm{X}=1) + \mathrm{P}(\mathrm{X}=2)\)…