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 $\frac{13}{20}$.
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