Question

If a students is selected random, then the probability that the has passed the examination is

• A. $1/7$
• B. $11/35$
• C. $11/14$
• D. $noneofthese$

Answer 1

The correct option is C $11/14$

Let P(i) be the probability that exactly i students are passing an examination.Now given that
$P\left(A_i\right)=\lambda i^2$ (where $\lambda$ is constant)
$\Rightarrow {\sum }_{i=1}^{10}P\left(A_i\right)={\sum }_{i=1}^{10}\lambda \frac{10\times 11\times 21}{6}=\lambda 385=1\Rightarrow \lambda \Rightarrow 1/385$

Let A represent the event that selected students have passed the examination.
$\therefore P\left(A\right)={\sum }_{i=1}^{10}P\left(A/A_i\right)P\left(A_i\right)$
$={\sum }_{i=1}^{10}\frac{i}{10}\frac{i^1}{385}$
$=\frac{1}{3850}{\sum }_{i=1}^{10}{i}^3$
$=\frac{{10}^2{11}^2}{4\times 3850}=\frac{11}{14}$