A mathematics book contains 400 pages. A page is selected at random. What is the probaility that the number on the page selected is a perfect square?

\frac{1}{30}

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\frac{1}{20}

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\frac{1}{40}

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None of these

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Solution

The correct option is B $\frac{1}{20}$
The perfect square before $400$ are $1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400$
Number of perfect squares are $20$
Total number of ways to select a perfect square is $^{20} C_{1} = 20$
Total number of ways to select a page is $^{400} C_{1} = 400$
Probability for this is $\frac{20}{400} = \frac{1}{20}$

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