Question:
A lot consists of 144 ball pens of which 20 are defective and the others are good.Rafia will buy a pen if it is good but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. The probability that she will buy that pen is
A lot consists of 144 ball pens of which 20 are defective and the others are good.Rafia will buy a pen if it is good but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. The probability that she will buy that pen is
Updated On: Apr 28, 2025
- \(\frac{5}{36}\)
- \(\frac{20}{36}\)
- \(\frac{31}{36}\)
- \(\frac{31}{144}\)
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The Correct Option is C
Approach Solution - 1
To find the probability that Rafia will buy the pen, we first need to identify the total number of pens and the number of pens that are good.
- The total number of pens in the lot is 144.
- The number of defective pens is 20.
- The number of good pens is calculated by subtracting the defective pens from the total number of pens: \(144 - 20 = 124\).
The probability that Rafia will buy a pen (i.e., picking a good pen) is given by the ratio of good pens to the total number of pens:
\[ \text{Probability} = \frac{\text{Number of Good Pens}}{\text{Total Number of Pens}} = \frac{124}{144} \]
Simplifying this fraction:
\[ \frac{124}{144} = \frac{31}{36} \]
Thus, the probability that Rafia will buy a pen is \(\frac{31}{36}\).
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Approach Solution -2
Given: A lot of 144 ball pens, where 20 are defective and the remaining are good.
Step 1: Understanding the Probability of Selecting a Good Pen
Total pens = 144
Defective pens = 20
Good pens = 144 - 20 = 124
Step 2: Probability Calculation
Probability of selecting a good pen = Number of good pens / Total number of pens
= 124 / 144 = 31 / 36
Final Answer: 31 / 36
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