CBSE2026Class Class 10 · Mathematics3 Marks · Short✅ Verified
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 ?
✅ Answer & Solution
PART 1 :
Step 1: Total pens $=200$, good pens $=180$.
Step 2: Number of defective pens
$$=200-180=20$$
Step 3: The customer will NOT buy the pen only if it is defective.
$$P(\text{customer will not buy})=\frac{20}{200}=\frac{1}{10}$$
PART 2 :
Step 4: Now a second lot of 100 pens (80 good) is mixed in. New total number of pens
$$=200+100=300$$
Step 5: New total number of good pens
$$=180+80=260$$
Step 6: The customer buys the pen if it is good.
$$P(\text{customer will buy})=\frac{260}{300}=\frac{13}{15}$$
Hence $P(\text{not buy})=\dfrac{1}{10}$ and $P(\text{buy})=\dfrac{13}{15}$.
