Class CBSE Class 12 Mathematics Probability Q #692
COMPETENCY BASED
APPLY
1 Marks 2025 AISSCE(Board Exam) MCQ SINGLE
A box has 4 green, 8 blue and 3 red pens. A student picks up a pen at random, checks its colour and replaces it in the box. He repeats this process 3 times. The probability that at least one pen picked was red is:
(A) \(\frac{124}{125}\)
(B) \(\frac{1}{125}\)
(C) \(\frac{61}{125}\)
(D) \(\frac{64}{125}\)
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Correct Answer: C

AI Tutor Explanation

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Step-by-Step Solution

Step 1: Calculate the total number of pens in the box.

Total pens = 4 (green) + 8 (blue) + 3 (red) = 15 pens

Step 2: Calculate the probability of picking a red pen in a single draw.

P(Red) = Number of red pens / Total number of pens = 3/15 = 1/5

Step 3: Calculate the probability of not picking a red pen in a single draw.

P(Not Red) = 1 - P(Red) = 1 - 1/5 = 4/5

Step 4: Calculate the probability of not picking a red pen in three consecutive draws (with replacement).

Since the pen is replaced each time, the draws are independent events.

P(Not Red in 3 draws) = (4/5) * (4/5) * (4/5) = (4/5)3 = 64/125

Step 5: Calculate the probability of picking at least one red pen in three draws.

This is the complement of not picking any red pens in three draws.

P(At least one Red) = 1 - P(Not Red in 3 draws) = 1 - 64/125 = (125 - 64) / 125 = 61/125

Correct Answer: \(\frac{61}{125}\)

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AI Suggestion: Option C

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the concepts of probability, specifically the probability of independent events and complementary events, to solve the problem. It requires using the formula for probability and applying it to a scenario.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure to calculate the probability. This involves identifying the total number of pens, calculating the probability of not picking a red pen in a single draw, and then using this to find the probability of not picking a red pen in three draws. Finally, the student must use the concept of complementary probability to find the probability of picking at least one red pen.
Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. The question assesses the student's ability to apply probability concepts to a real-world scenario, rather than simply recalling definitions or formulas. It requires problem-solving skills and the ability to connect different concepts.

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