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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Probability

NDA 2021 · Mathematics · Probability

In a binomial distribution, the mean is (2)/(3) and variance is...

In a binomial distribution, the mean is 23\frac{2}{3} and variance is 59\frac{5}{9}. What is the probability that random variable X=2X=2 ?

Options

  1. A536\frac{5}{36}
  2. B2536\frac{25}{36}
  3. C2554\frac{25}{54}
  4. D25216\frac{25}{216}

Correct answer

D. 25216\frac{25}{216}

Step-by-step solution

Mean (np)=23Variance⁡(npq)=59∴ Variance (npq)mean⁡(np)=q=5923=56p=1−q=1−56=16(n p)=\frac{2}{3}\operatorname{Variance}(n p q)=\frac{5}{9}\therefore \quad \frac{\text{ Variance }(n p q)}{\operatorname{mean}(n p)}=q=\frac{\frac{5}{9}}{\frac{2}{3}}=\frac{5}{6}p=1-q=1-\frac{5}{6}=\frac{1}{6} Here number of trial n×16=23n \times \frac{1}{6}=\frac{2}{3} Random Variable X=2∴X=2\therefore \quad Probability =4C2(P)4−2Q2=4C2×(16)2×(56)2=25216={ }^4 \mathrm{C}_2(\mathrm{P}){ }^{4-2} \mathrm{Q}^2={ }^4 C_2 \times\left(\frac{1}{6}\right)^2 \times\left(\frac{5}{6}\right)^2=\frac{25}{216}
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