There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified. Then, the probability that only two tests are needed, is

Question

There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified. Then, the probability that only two tests are needed, is (A) (1/3) (B) (1/6) (C) (1/2) (D) (1/4)

Tardigrade Admin · Accepted Answer

Probability that only two tests are needed = Probability that the first machine tested is faulty × Probability that the second machine tested is faulty =(2/4) × (1/3)=(1/6)

Q. There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified. Then, the probability that only two tests are needed, is

$\frac{1}{3}$

$\frac{1}{6}$

$\frac{1}{2}$

$\frac{1}{4}$

Probability that only two tests are needed = Probability that the first machine tested is faulty $\times$ Probability that the second machine tested is faulty
= $\frac{2}{4} \times \frac{1}{3} = \frac{1}{6}$