NIMCET 2013
Person A can hit a target 4 times in 5 attempts, person B 3 times in 4 attempts and person C 2 times in 3 attempts. They fire a volley. The probability that the target is hit at least two times is
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Answer: Option C — 5/6
Detailed Solution
Hit probabilities , , ; miss probabilities , , .
Exactly two hits: .
All three hit: . At least two: .
✓ Check
Exactly one hit is and no hit is ; .⚠ Common trap
(D) 1 would mean the volley can never hit fewer than twice, but all three miss with probability .Quick tip
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Probability — Preparation
This question tests your understanding of Probability, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
Probability measures how likely an event is, as a number between 0 and 1. It equals the number of favourable outcomes divided by the total number of possible outcomes, when all outcomes are equally likely. This topic covers coins, dice, playing cards, drawing balls from a bag, complementary events, independent events, and conditional probability. The most useful tools are the complement rule (P(at least one) = 1 - P(none)) and the multiplication rule for independent events. For engineering and MCA entrance exams, the topic also includes the addition theorem, conditional probability, Bayes' theorem, and probability distributions. A clear sample space is the key to avoiding mistakes, so always list or count all outcomes carefully. Practise the probability questions below. Each comes with a step-by-step solution that shows how the sample space and favourable outcomes are counted.