ProbabilityMCQMTP May 20Question 2819 of 295
All Questions

Rupesh is known to hit a target in 5 out of 9 shots whereas David is known to hit the same target in 6 out of 11 shots. What is the probability that the target would be hit once they both try?

Options

A7999\displaystyle \frac{79}{99}
B1013\displaystyle \frac{10}{13}
C1426\displaystyle \frac{14}{26}
D1318\displaystyle \frac{13}{18}
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — 7999\displaystyle \frac{79}{99}

All Options:

  • A7999\displaystyle \frac{79}{99}
  • B1013\displaystyle \frac{10}{13}
  • C1426\displaystyle \frac{14}{26}
  • D1318\displaystyle \frac{13}{18}

Ad

Detailed Solution & Explanation

Let R\displaystyle R represent the event that Rupesh hits the target, and D\displaystyle D represent the event that David hits the target. 1. The individual probabilities of hitting the target are: - P(R)=59\displaystyle P(R) = \frac{5}{9} - P(D)=611\displaystyle P(D) = \frac{6}{11} 2. The probabilities of failing to hit the target are: - P(R′)=1−59=49\displaystyle P(R') = 1 - \frac{5}{9} = \frac{4}{9} - P(D′)=1−611=511\displaystyle P(D') = 1 - \frac{6}{11} = \frac{5}{11} 3. Assuming their shots are independent, the probability that neither of them hits the target is: P(Neither hits)=P(R′)×P(D′)=49×511=2099P(\text{Neither hits}) = P(R') \times P(D') = \frac{4}{9} \times \frac{5}{11} = \frac{20}{99} 4. The probability that the target is hit (at least one hits it) is: P(Target is hit)=1−P(Neither hits)=1−2099=7999P(\text{Target is hit}) = 1 - P(\text{Neither hits}) = 1 - \frac{20}{99} = \frac{79}{99} 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 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.

More Questions from Probability

Mode can be obtained from________

The modes of presentation of data are:

The distribution of income is an example of frequency distribution of

In a frequency distribution, the relative frequency of the class is:

Histogram can be drawn when

Less than ‘o’give curve give

Ready to Master Probability?

Practice all 295 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free