Ram is known to hit a target in $2$ out of $3$ shots where as Shyam is known to hit the same target in $5$ out of $11$ shots. What is the probability that the target would be hit if they both try?

The correct answer is Option a: $\frac{3}{7}$. PYQ Oct 03

ProbabilityPYQ Oct 03Question 3314 of 170

Ram is known to hit a target in $\displaystyle 2$ out of $\displaystyle 3$ shots where as Shyam is known to hit the same target in $\displaystyle 5$ out of $\displaystyle 11$ shots. What is the probability that the target would be hit if they both try?

Options

\displaystyle \frac{3}{7}

\displaystyle \frac{2}{3}

\displaystyle \frac{10}{33}

\displaystyle \frac{6}{11}

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Correct Answer

✅ Option a — $\displaystyle \frac{3}{7}$

All Options:

A $\displaystyle \frac{3}{7}$
B $\displaystyle \frac{2}{3}$
C $\displaystyle \frac{10}{33}$
D $\displaystyle \frac{6}{11}$

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.

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Ram is known to hit a target in 2\displaystyle 22 out of 3\displaystyle 33 shots where as Shyam is known to hit the same target in 5\displaystyle 55 out of 11\displaystyle 1111 shots. What is the probability that the target would be hit if they both try?