Class CBSE Class 12 Mathematics Probability Q #828
KNOWLEDGE BASED
UNDERSTAND
1 Marks 2023 MCQ SINGLE
Five fair coins are tossed simultaneously. The probability of the events that atleast one head comes up is
(A) 27/32
(B) 5/32
(C) 31/32
(D) 1/32
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AI Tutor Explanation

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Step-by-Step Solution

  1. First, find the total number of possible outcomes when tossing five coins. Each coin has 2 possible outcomes (Heads or Tails), so for five coins, the total number of outcomes is 25 = 32.

  2. Next, find the probability of the complementary event: no heads (i.e., all tails). There is only one way for this to happen (TTTTT).

  3. The probability of getting all tails is 1/32.

  4. The probability of getting at least one head is 1 minus the probability of getting all tails.

  5. Therefore, P(at least one head) = 1 - P(all tails) = 1 - (1/32) = 31/32.

Correct Answer: 31/32

AI Suggestion: Option C

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Pedagogical Audit
Bloom's Analysis: This is an UNDERSTAND question because it requires the student to comprehend the concept of probability and apply it to a specific scenario involving coin tosses. The student needs to understand how to calculate the probability of complementary events.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of probability concepts, specifically the probability of complementary events (at least one head vs. no heads). It requires the student to grasp the underlying principles rather than just recalling facts or following a specific algorithm.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly assesses the student's understanding of probability as covered in the textbook and syllabus. It does not require application to a novel or real-world scenario, but rather a direct application of learned concepts.

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