Question
Question: There are four machines and it is known that exactly two of them are faulty. They are tested one by ...
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. 31
B. 61
C. 21
D. 41
Solution
Hint : Recall the concepts of probability and the formula to find the probability of an event. We are asked to find the probability to find out the faulty ones in just two tests. Check for all the possible cases, find the probability of each case and combine them to find the required probability.
Complete step-by-step answer :
Given, total number of machines T=4
Number of faulty machines F=2
Total number of tests, S=2
Let us find the number of working machines.
Number of working machines will be,
W=T−F
Putting the values of T and F we get