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  • The chances of defective screw in three boxes A, B, C are  <img alt="\frac{1}{5},\frac{1}{6},\frac{1}{7}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cfrac%7B1%7D%7B5%7D%2C%5Cfrac%7

The chances of defective screw in three boxes A, B, C are  \frac{1}{5},\frac{1}{6},\frac{1}{7} respectively. A box is selected at random and a screw is drawn from it at random, is found to be defective, then the probability that it came from box A is

 

 

Option: 1

\frac{42}{107}


Option: 2

\frac{4}{107}


Option: 3

\frac{2}{107}


Option: 4

\frac{1}{7}


Answers (1)

Answer (1)

P(D_A)=\frac{1}{5},P(D_B)=\frac{1}{6},P(D_C)=\frac{1}{7}\\ \\E : f\! or\; selecting \; any \; box, \\ \\ P(A)=\frac{1}{3}=P(B)=P(C)\\ \\ P(D)_A=\frac{\frac{1}{5}\times \frac{1}{3}}{\frac{1}{5}\times \frac{1}{3}+\frac{1}{6}\times \frac{1}{7}+\frac{1}{7}\times \frac{1}{3}}= \frac{42}{107}

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Kshitij

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