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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 now 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 $\frac{13}{15}$