Question

There are four EVMs in a polling centre. It is known that two of them are fixed. They are tested one by one in a random orders till both the faulty EVMs are identified. The probability that only two tests are needed to identify such machines is---

• A. $\frac{1}{6}$
• B. $\frac{1}{9}$
• C. $\frac{4}{9}$
• D. $\frac{1}{3}$

Answer 1

The correct option is A $\frac{1}{6}$

No. of EVMs in a polling center $=4$

They are test randomly in one by one order,

$\Rightarrow {}^n{C}_r{p}^r{q}^r$ where $p=\frac{1}{4}$ $q=\frac{3}{4}$ $n=4$

$\Rightarrow {}^4{C}_2{\left(\frac{1}{4}\right)}^2{\left(\frac{3}{4}\right)}^2=0.56$

$\Rightarrow$ The probability that only $2$ tests were conducted $=\frac{2}{5}=0.4$

$\therefore$ Total probability $=0.56-0.4=\mathrm{0.16.}$

Hence, the answer is $\frac{1}{6}.$