The probability that there is at least one error in an account statement prepared by 3 persons A, B and C are 0.2 , 0.3 and 0.1 respectively. If A, B and C prepare 60 , 70 and 90 such statements, then the expected number of correct statements

Option c: 178. Solution: Expected Number of Correct Statements Let's find the probability of a correct statement for each person: - For A: Probability of error is 0.2 ⟹ Probability of correct statement is 1 - 0.2 = 0.8 . - For B: Probability of error is 0.3 ⟹ Probability of correct statement is 1 - 0.3 = 0.7 . - For C: Probability of error is 0.1 ⟹ Probability of correct statement is 1 - 0.1 = 0.9 . Now, calculate the expected number of correct statements for each: - Expected correct statements by A: 60 × 0.8 = 48 - Expected correct statements by B: 70 × 0.7 = 49 - Expected correct statements by C: 90 × 0.9 = 81 Total expected correct statements: Total = 48 + 49 + 81 = 178 Hence, Option C is the correct answer.

The probability that there is at least one error in an account statement prepared by $3$ persons A, B and C are $0.2$, $0.3$ and $0.1$ respectively. If A, B and C prepare $60$, $70$ and $90$ such statements, then the expected number of correct statements

The correct answer is Option c: $178$. **Expected Number of Correct Statements** Let's find the probability of a correct statement for each person: - For A: Probability of error is $0.2 \Rightarrow$ Probability of correct statement is $1 - 0.2 = 0.8$. - For B: Probability of error is $0.3 \Rightarrow$ Probability of correct statement is $1 - 0.3 = 0.7$. - For C: Probability of error is $0.1 \Rightarrow$ Probability of correct statement is $1 - 0.1 = 0.9$. Now, calculate the expected number of correct statements for each: - Expected correct statements by A: $60 \times 0.8 = 48$ - Expected correct statements by B: $70 \times 0.7 = 49$ - Expected correct statements by C: $90 \times 0.9 = 81$ Total expected correct statements: $$\text{Total} = 48 + 49 + 81 = 178$$ Hence, **Option C** is the correct answer.

ProbabilityMCQMTP March 22Question 3386 of 187

All Questions

The probability that there is at least one error in an account statement prepared by $\displaystyle 3$ persons A, B and C are $\displaystyle 0.2$ , $\displaystyle 0.3$ and $\displaystyle 0.1$ respectively. If A, B and C prepare $\displaystyle 60$ , $\displaystyle 70$ and $\displaystyle 90$ such statements, then the expected number of correct statements

Options

\displaystyle 170

\displaystyle 176

\displaystyle 178

\displaystyle 180

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Correct Answer

✅ Option c — $\displaystyle 178$

All Options:

A $\displaystyle 170$
B $\displaystyle 176$
C $\displaystyle 178$
D $\displaystyle 180$

Detailed Solution & Explanation

**Expected Number of Correct Statements** Let's find the probability of a correct statement for each person: - For A: Probability of error is

\displaystyle 0.2 \Rightarrow

Probability of correct statement is

\displaystyle 1 - 0.2 = 0.8

. - For B: Probability of error is

\displaystyle 0.3 \Rightarrow

Probability of correct statement is

\displaystyle 1 - 0.3 = 0.7

. - For C: Probability of error is

\displaystyle 0.1 \Rightarrow

Probability of correct statement is

\displaystyle 1 - 0.1 = 0.9

. Now, calculate the expected number of correct statements for each: - Expected correct statements by A:

\displaystyle 60 \times 0.8 = 48

- Expected correct statements by B:

\displaystyle 70 \times 0.7 = 49

- Expected correct statements by C:

\displaystyle 90 \times 0.9 = 81

Total expected correct statements:

\text{Total} = 48 + 49 + 81 = 178

Hence, **Option C** 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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