One card is drawn at random from 100 cards numbered 1 to 100. What is the probability that the number is a perfect square?
Aptitude
Probability
Difficulty: Easy
Choose an option
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A1/5
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B2/5
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C1/10
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DNone of these
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E3/10
Answer
Correct Answer: 1/10
Explanation
Introduction / Context:Perfect squares ≤ 100 occur at n^2 for n = 1,…,10. The sample space contains 100 equally likely outcomes. We count and divide.
Given Data / Assumptions:
- Numbers 1 to 100 equiprobable.
- Squares: 1,4,9,16,25,36,49,64,81,100.
Concept / Approach:Count favorable outcomes, then compute probability = favorable / total.
Step-by-Step Solution:
Favorable squares = 10.Total outcomes = 100.Probability = 10/100 = 1/10.Verification / Alternative check:Because 100 = 10^2, there are exactly 10 perfect squares up to 100. The list confirms the count.
Why Other Options Are Wrong:1/5 (= 0.2) and 2/5 (= 0.4) overestimate; “None of these” is unnecessary as 1/10 is exact.
Common Pitfalls:Including 0 (not in range) or omitting 100 (which is 10^2).
Final Answer:1/10