A box contains 90 discs which are numbered from 1 to 90. If one discs is drawn at random from the box, find the probability that it bears a perfect square number.
Given:
A box contains 90 discs which are numbered from 1 to 90.
One disc is drawn at random from the box.
To do:
We have to find the probability that it bears a perfect square number.
Solution:
A box contains discs numbered \( 1,2,3,4, .., 89,90 \).
This implies,
The total number of possible outcomes $n=90$.
Perfect square numbers from 1 to 90 are $1, 4, 9, 16, 25, 36, 49, 64, 81$.
Total number of favourable outcomes $=9$.
We know that,
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability that the disc bears a perfect square number $=\frac{9}{90}$
$=\frac{1}{10}$
The probability that it bears a perfect square number is $\frac{1}{10}$.
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