Question 16 of 55beginner🔧 ApplyShort Answer2 marks

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.

Correct Answer

To find the probability of drawing a good pen, we first determine the total number of pens in the lot. The total number of pens is the sum of defective and good pens: 12+132=14412 + 132 = 144. Since the pen is drawn at random, there are 144 equally likely outcomes.

Next, we identify the number of favourable outcomes. The event is drawing a good pen. Given that there are 132 good pens, the number of favourable outcomes is 132. Finally, the probability of the event is calculated using the formula: P(Event)=Number of favourable outcomesTotal number of outcomesP(\text{Event}) = \frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}. Therefore, P(Good Pen)=132144P(\text{Good Pen}) = \frac{132}{144}. Simplifying the fraction by dividing by 12, we get 1112\frac{11}{12}.

Exercise: EXERCISE 14.1 | Q: 16 | (Page Page 14)
For More Understanding

Explanation

This question applies the fundamental definition of probability provided in the textbook context (specifically referenced in Example 12). The probability is the ratio of the number of favourable outcomes (good pens) to the total number of outcomes (total pens). The calculation involves simple addition to find the total and fraction simplification.

Solution Steps

  1. Step 1: Calculate the Total number of pens by adding defective and good ones: 12+132=14412 + 132 = 144.

  2. Step 2: Identify the Number of favourable outcomes (good pens), which is 132.

  3. Step 3: Calculate Probability using the formula P(Good Pen)=132144P(\text{Good Pen}) = \frac{132}{144}.

  4. Step 4: Simplify the fraction by dividing numerator and denominator by 12 to get 1112\frac{11}{12}.

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