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.
The total number of pens in the lot is the sum of defective and good pens. Since the pen is drawn at random, all outcomes are equally likely.
Total number of pens = Number of defective pens + Number of good pens = 12 + 132 = 144.
Number of favourable outcomes corresponds to the event that the pen taken out is a good one. There are 132 good pens.
Therefore, Probability (getting a good pen) = Number of favourable outcomes / Total number of outcomes = 132 / 144 = 11/12.
Explanation
This solution follows the standard probability formula P(E) = Number of favourable outcomes / Total number of possible outcomes, as demonstrated in Example 12 of the provided context. The total number of possible outcomes is the sum of all pens (defective + good), and the favourable outcomes are the specific pens being counted (good ones).
Solution Steps
Step 1: Calculate the Total number of pens by adding defective and good pens: 12 + 132 = 144.
Step 2: Identify the Number of favourable outcomes (good pens), which is 132.
Step 3: Calculate Probability using the formula: P(good pen) = 132 / 144.
Step 4: Simplify the fraction by dividing numerator and denominator by 12 to get 11/12.