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A lot consists of $200$ pens of which $180$ are good and the rest are defective. A customer will buy a pen if it is not defective. The shopkeeper draws a pen at random and gives it to the customer. What is the probability that the customer will not buy it ? Another lot of $100$ pens containing $80$ good pens is mixed with the previous lot of $200$ pens. The shopkeeper draws one pen at random from the entire lot and gives it to the customer. What is the probability that the customer will buy the pen ?
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Solution: $P(\text{customer will not buy the pen}) = \frac{20}{200} = \frac{1}{10}$
After mixing the two lots
Total pens $= 200 + 100 = 300$
Number of good pens $= 180 + 80 = 260$
$P(\text{customer will buy the pen}) = \frac{260}{300}$ or $\frac{13}{15}$
After mixing the two lots
Total pens $= 200 + 100 = 300$
Number of good pens $= 180 + 80 = 260$
$P(\text{customer will buy the pen}) = \frac{260}{300}$ or $\frac{13}{15}$