# A box contains cards numbered $3,5,7,9, .., 35,37$. 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 cards numbered $3,5,7,9, .., 35,37$.

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:

A box contains cards numbered $3,5,7,9, .., 35,37$.

This implies,

The total number of possible outcomes $n=18$.

Prime numbers from 3 to 37 are $3, 5, 7, 11, 13, 17, 19, 23, 29, 31$ and $37$.

Total number of favourable outcomes $=11$.

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 $=\frac{11}{35}$

$=\frac{11}{18}$

The probability that the number on the drawn card is a prime number is $\frac{11}{18}$.

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Updated on: 10-Oct-2022

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