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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 divisible by 3.
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 divisible by 3.
Solution:
Total number of cards $=30$
This implies,
The total number of possible outcomes $n=30$.
Numbers divisible by 3 from 1 to 30 are 3, 6, 9, 12, 15, 18, 21, 24, 27 and 30.
Total number of numbers divisible by 3 from 1 to 30 $=10$
Total number of numbers not divisible by 3 from 1 to 30 $=30-10=20$
Total number of favourable outcomes $=20$.
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 divisible by 3 $=\frac{20}{30}$
$=\frac{2}{3}$
The probability that the number on the drawn card is not divisible by 3 is $\frac{2}{3}$.