There are four machines and it is known that | vedclass

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Question

(b) This is a problem of without replacement.

$P = \frac{{{\rm{one}}\,{\rm{def}}\,{\rm{.}}\,{\rm{from}}\,2\,{\rm{def}}{\rm{.}}}}{{{\rm{any}}\,{\rm{

Vedclass · Accepted Answer

$\frac{1}{6}$

Vedclass · Answer

(b) This is a problem of without replacement.

$P = \frac{{{m{one}}\,{m{def}}\,{m{.}}\,{m{from}}\,2\,{m{def}}{m{.}}}}{{{m{any}}\,{m{one}}\,{m{from}}\,4}} 	imes \frac{{1\,{m{def}}\,{m{.}}\,{m{from}}\,{m{remaining}}\,{m{1}}\,{m{def}}{m{.}}}}{{{m{any}}\,{m{one}}\,{m{from}}\,{m{remaining}}\,3}}$

Hence required probability $ = \frac{2}{4} 	imes \frac{1}{3} = \frac{1}{6}$

Aliter : Number of ways in which two faulty machines may be detected (depending upon the test done to indentify the faulty machines) $ = {}^4{C_2} = 6$

Number of favourable cases = $1$

[When faulty machines are identified in the first and the second test]

Hence required probability $ = \frac{1}{6}.$

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

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