A card is drawn at random from a pack of 100 cards numbered 1 to 100. The probability of drawing a number which is a square, is

Question

A card is drawn at random from a pack of 100 cards numbered 1 to 100. The probability of drawing a number which is a square, is

1. A. 1/10 (Correct answer)
2. B. 1/100
3. C. 9/10
4. D. 90/100

Correct Answer

Option A — 1/10

Detailed Solution & Explanation

The correct answer is 1/10.

Key Points

• This is a probability question.
• The formula is P = favourable outcomes ÷ total outcomes.
• The pack has cards numbered 1 to 100, so the total number of outcomes = 100.
• The perfect squares from 1 to 100 are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 — that is 1² up to 10², giving 10 favourable outcomes.
• So P(square) = 10 ÷ 100 = 1/10.
• the count of perfect squares from 1 to N equals the integer part of √N; here √100 = 10, so there are exactly 10 squares.
• Listing them also avoids missing 1 or 100, which candidates often overlook.

Exam Tip

• for 'number from 1 to 100' probability questions, memorise the counts — 10 squares, 4 cubes (1,8,27,64), 25 primes — so you can answer instantly without listing.