Question

# 12 defective pens are accidentally mixed up the 132 good ones. It is not possible to just look at a pen and tell whether it is defective or not. One pen is taken out at random from the lot. Find the probability that the pen taken out is (i) a good one, (ii) defective

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Solution

## Number of defective pens in the lot = 12 Number of good pens in the lot = 132 Total number of pens in the lot = 12 + 132 = 144 ∴ Total number of outcomes = 144 (i) There are 132 good pens in the lot. Out of these pens, one good pen can be taken out in 132 ways. Favourable number of outcomes = 132 ∴ P(Pen taken out is good one) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{132}{144}=\frac{11}{12}$ (ii) There are 12 defective pens in the lot. Out of these pens, one defective pen can be taken out in 12 ways. Favourable number of outcomes = 12 ∴ P(Pen taken out is defective) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{12}{144}=\frac{1}{12}$

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