A card is drawn from a pack of 100 cards numbered 1 to 100. The probability of…
2022
A card is drawn from a pack of 100 cards numbered 1 to 100. The probability of drawing a number which is square, is
- A.
1/20
- B.
11/100
- C.
9/10
- D.
1/10
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Correct answer: D
Concept: When all outcomes are equally likely, probability = (number of favourable outcomes) / (total number of outcomes). A perfect square is a number of the form n2 for a positive integer n.
The pack has 100 cards numbered 1 to 100, and each card is equally likely to be drawn, so the total number of outcomes is 100.
Check each base n = 1, 2, 3, ... : n2 stays within 100 as long as n ≤ 10, since 102 = 100 but 112 = 121 exceeds 100. So the favourable outcomes are 12, 22, 32, ..., 102, i.e. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 — 10 numbers in all.
Probability = favourable outcomes / total outcomes = 10/100 = 1/10.
Cross-check: The count of perfect squares from 1 to N always equals ⌊√N⌋. Here ⌊√100⌋ = 10, which matches the count found above, confirming the probability is 1/10.