ProbabilityMCQMTP Nov 21Question 2806 of 295

Two different dice are thrown simultaneously, then the probability, that the sum of two numbers appearing on the top of dice 9 is

Options

\displaystyle \frac{8}{9}

\displaystyle \frac{1}{9}

\displaystyle \frac{7}{9}

DNone of these

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Correct Answer

✅ Option b — $\displaystyle \frac{1}{9}$

All Options:

A $\displaystyle \frac{8}{9}$
B $\displaystyle \frac{1}{9}$
C $\displaystyle \frac{7}{9}$
DNone of these

Detailed Solution & Explanation

When two dice are thrown simultaneously: 1. **Total number of possible outcomes** is:

6 \times 6 = 36

2. Let the outcome on the first die be

\displaystyle x

and the second die be

\displaystyle y

. We want to find the outcomes where the sum

\displaystyle x + y = 9

. 3. The pairs

\displaystyle (x, y)

that sum up to 9 are: -

\displaystyle (3, 6)

\displaystyle (4, 5)

\displaystyle (5, 4)

\displaystyle (6, 3)

4. Therefore, the number of favorable outcomes is 4. 5. The probability that the sum of two numbers is 9 is:

\text{Probability} = \frac{4}{36} = \frac{1}{9}

Hence, **Option B** 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 Syllabus

Exam 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

Probability

A numerical measure of the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). Formula: P(A) = Number of favorable outcomes / Total number of equally likely outcomes.

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