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A page is opened at random from a book containing 90 pages. Then the probability of a page number is a perfect square, is ___.

Last updated date: 13th Jun 2024
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Hint:In the above question, number of pages in the book is 90 pages which would be taken as Total cases. Number of perfect squares between 1 to 90 is the favorable case. So, the probability of a page number is equal to the number of perfect squares (favorable cases) divided by total cases.

Complete step-by-step answer:
Number of pages in the book that is total cases = 90 pages
Number of perfect squares from 1 to 90 are 1, 4, 9, 16, 25, 36, 49, 64, 81.
Favorable cases, that is number of perfect squares between 1 to 90 = 9
[Probability is defined as the ratio of number of favourable outcomes to the number of total possible outcomes]
Probability of a page number is a perfect square $ = \dfrac{9}{{90}} = \dfrac{1}{{10}}$
Therefore, probability is $\dfrac{1}{{10}}$.

So, the correct answer is “Option A”.

Note:Probability can also be called as possibility.It is expressed between 0 to 1, where 0 means the event is impossible and 1 means an event is certain. Probability is the measure of an event to occur. The probability of all the events in a sample space is equal to 1. For example – When a die is thrown, there are six possible outcomes – 1, 2, 3, 4, 5, 6. Then the probability of any one of them is $\dfrac{1}{6}$. In general, the probability of an event happening is the number of ways it can happen divided by the total number of outcomes.