12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.
Step-by-Step Solution
Key Concept: Use the classical definition of probability: \(P(E) = \frac{\text{Number of favourable outcomes}}{\text{Total number of equally likely outcomes}}\). Here, the favourable outcomes are the good pens.
1. Total number of pens in the lot = defective pens + good pens = $12 + 132 = 144$.
2. Number of favourable outcomes (good pens) = $132$.
3. Apply the probability formula:
$$P(\text{good pen}) = \frac{\text{Number of good pens}}{\text{Total pens}} = \frac{132}{144}.$$
4. Simplify the fraction:
$$\frac{132}{144} = \frac{132 \div 12}{144 \div 12} = \frac{11}{12}.$$
5. Result: The probability that the randomly drawn pen is good is $\frac{11}{12}$ (approximately $0.917$).
Correct Answer: \(\frac{11}{12}\)