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Cards numbered 1 to 30 are put in a bag. A card is drawn at random from this bag. Find the probability that the number on the drawn card is not a perfect square number.
Given:
Cards numbered 1 to 30 are put in a bag. A card is drawn at random from this bag.
To do:
We have to find the probability that the number on the drawn card is not a perfect square number.
Solution:
Total number of cards $=30$
This implies,
The total number of possible outcomes $n=30$.
Perfect square numbers from 1 to 30 are 1, 4, 9, 16 and 25.
Total number of numbers which are not perfect square numbers from 1 to 30 $=30-5=25$
Total number of favourable outcomes $=25$.
We know that,
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability that the number on the drawn card is not a perfect square number $=\frac{25}{30}$
$=\frac{5}{6}$
The probability that the number on the drawn card is not a perfect square number is $\frac{5}{6}$.