There are 30 cards, of same size, in a bag on which numbers 1 to 30 are written. One card is taken out of the bag at random. Find the probability that the number on the selected card is not divisible by 3.
Given:

There are 30 cards, of same size, in a bag on which numbers 1 to 30 are written. One card is taken out of the bag at random.

To do:

We have to find the probability that the number on the selected 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 selected card is not divisible by 3 $=\frac{20}{30}$

$=\frac{2}{3}$

The probability that the number on the selected card is not divisible by 3 is $\frac{2}{3}$.

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