# 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 a prime number.

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 a prime number.

Solution:

Total number of cards $=20$

This implies,

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

Prime numbers from 1 to 20 are 2, 3, 5, 7, 11, 13, 17 and 19.

Total number of prime numbers from 1 to 20 $=8$

Total number of favourable outcomes $=8$.

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 a prime number $=\frac{8}{20}$

$=\frac{2}{5}$

The probability that the number on the drawn card is a prime number is $\frac{2}{5}$.

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Updated on: 10-Oct-2022

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