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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
(a) 1/5
(b) 2/5
(c) 1/10
(d) none of these

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Solution

(c) 1/10

Clearly, the sample space is given by
S = {1, 2, 3, 4, 5... 97, 98, 99, 100}
∴ n(S) = 100
Let E = event of getting a square.
Then E = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100}
∴ n(E) = 10
Hence, required probability = nEnS=10100=110

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