Statistics And Probability Question 11
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
Options:
A) $ \frac{1}{3} $
B) $ \frac{1}{6} $
C) $ \frac{1}{2} $
D) $ \frac{1}{4} $
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Answer:
Correct Answer: A
Solution:
- [a] The faulty machines can be identified in two tests only if both the tested machines are either all defective or all non-defective. See the following tree diagram. (Here D is for defective & ND is for non-defective) Reqd. Probability $ =\frac{2}{4}\times \frac{1}{3}+\frac{2}{4}\times \frac{1}{3}=\frac{1}{3} $
$ \therefore $ The probability that first machine is defective (or non-defective) is $ \frac{2}{4} $ and the probability that second machine is also defective (or non-defective) is $ \frac{1}{3} $ as 1 defective machine remains in total three machines.
BETA
