A box contains 20 cards numbered from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the drawn card is divisible by 2 or 3.

 Given:

A box contains 20 cards numbered from 1 to 20. A card is drawn at random from the box.

To do:

We have to find the probability that the number on the drawn card is divisible by 2 or 3.

Solution:

Total number of cards $=20$

This implies,

The total number of possible outcomes $n=20$.

Numbers divisible by 2 from 1 to 20 are 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20.

Numbers divisible by 3 from 1 to 20 are 3, 6, 9, 12, 15 and 18.

Total number of numbers divisible by 2 or 3 from 1 to 20 $=10+6-3=13$

Total number of favourable outcomes $=13$.

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 divisible by 2 or 3 $=\frac{13}{20}$

The probability that the number on the drawn card is divisible by 2 or 3 is $\frac{13}{20}$.