There are four machines and it is known that | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the four machines be $M_1, M_2, F_1, F_2$,where $F$ denotes a faulty machine and $M$ denotes a working machine.We need to find the probability

Vedclass · Accepted Answer

$\frac{1}{6}$

Vedclass · Answer

(B) Let the four machines be $M_1, M_2, F_1, F_2$,where $F$ denotes a faulty machine and $M$ denotes a working machine.We need to find the probability that both faulty machines are identified in exactly two tests.This means the first test must result in a faulty machine,and the second test must also result in a faulty machine.The total number of ways to choose $2$ machines out of $4$ for the first two tests is $^4P_2 = 4 	imes 3 = 12$.The number of ways to choose $2$ faulty machines out of $2$ for the first two tests is $^2P_2 = 2 	imes 1 = 2$.Therefore,the required probability is $\frac{2}{12} = \frac{1}{6}$.Alternatively,the probability that the first machine tested is faulty is $\frac{2}{4}$.Given that the first machine was faulty,the probability that the second machine tested is also faulty is $\frac{1}{3}$.Thus,the required probability is $\frac{2}{4} 	imes \frac{1}{3} = \frac{1}{6}$.

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 until both the faulty machines are identified. Then the probability that only two tests are needed is

Similar Questions

Five horses are in a race. $Mr. A$ selects two of the horses at random and bets on them. The probability that $Mr. A$ selected the winning horse is

$5$ boys and $5$ girls are sitting in a row randomly. The probability that boys and girls sit alternatively is

There are $n$ letters and $n$ addressed envelopes. The probability that each letter is placed in the correct envelope is

$A$ $5$-digit number is formed using the digits $1, 2, 3, 4, 5, 6,$ and $8$. What is the probability that the number has even digits at both ends?

If five-digit numbers are formed from the digits $0, 1, 2, 3, 4$ using every digit exactly once,then the probability that a randomly chosen number from those numbers is divisible by $4$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module