Question

There are four machines and it is known that exactly two of them are faulty machines and are to be identified. Then the probability that only two tests are needed is:

• A. $\frac{1}{3}$
• B. $\frac{1}{6}$
• C. $\frac{1}{2}$
• D. $\frac{1}{4}$

Answer 1

The correct option is A $\frac{1}{3}$

Only two tests are required when the two machines tested are either both working or both are not working.
Case $:1$ Both are working.
Probability $=\frac{2}{4}\times \frac{1}{3}=\frac{1}{6}$
Case $:2$ Both are not working.
Probability $=\frac{2}{4}\times \frac{1}{3}=\frac{1}{6}$
Hence, Total probability that only test are required is
$=\frac{1}{6}+\frac{1}{6}=\frac{1}{3}$