If two dice are rolled and one of the dice shows 1 at a point then how many such outcome can be done where it is known that its probability is where
Options
A
B
C
D
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ProbabilityMCQPYQ Dec. 21Question 2838 of 295
All Questions Correct Answer
✅ Option a —
All Options:
- A
- B
- C
- D
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Detailed Solution & Explanation
When two fair six-sided dice are rolled, the sample space consists of equally likely outcomes.
We want to find how many outcomes contain at least one die showing the number 1.
Let's list these outcomes:
- First die shows 1: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6) (6 outcomes)
- Second die shows 1: (2,1), (3,1), (4,1), (5,1), (6,1) (5 outcomes, excluding (1,1) since it is already counted)
Combining these, there are:
such outcomes.
Since each outcome in the sample space has a probability of , there are exactly 11 outcomes matching this condition.
Hence, **Option A** is the correct answer.
About This Chapter: Probability
Paper
Paper 3: Quantitative Aptitude
Weightage
5-7 Marks
Key Topics
Probability Operations, Expected Value
A logic-heavy chapter dealing with random experiments, events (mutually exclusive, exhaustive), set theory probability, conditional probability, and Bayes' Theorem. It forms the basis for Theoretical Distributions.
View Official ICAI SyllabusExam Strategy Tip
Always draw a quick Venn Diagram or tree when faced with 'At least one' or 'Only A but not B' wording. It saves you from double-counting.
Key Concepts to Understand
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