Cards numbered 1 to 30 are put in a bag. A card is drawn at random from this bag. Find the probability that the number on the drawn card is a prime number great than 7.

 Given:

Cards numbered 1 to 30 are put in a bag. A card is drawn at random from this bag.

To do:

We have to find the probability that the number on the drawn card is a prime number great than 7.

Solution:

Total number of cards $=30$

This implies,

The total number of possible outcomes $n=30$.

Prime numbers greater than 7 from 1 to 30 are 11, 13, 17, 19, 23 and 29.

Total number of prime numbers greater than 7 from 1 to 30 $=6$

Total number of favourable outcomes $=6$.

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 great than 7 $=\frac{6}{30}$

$=\frac{1}{5}$

The probability that the number on the drawn card is a prime number greater than 7 is $\frac{1}{5}$.