A bag contains tickets numbered $ 11,12,13, \ldots, 30 $. A ticket is taken out from the bag at random. Find the probability that the number on the drawn ticket is a multiple of 7.

Given:

A bag contains tickets numbered \( 11,12,13, \ldots, 30 \). A ticket is taken out from the bag at random.

To do:

We have to find the probability that the number on the drawn ticket is a multiple of 7.

Solution:

A bag contains tickets numbered \( 11,12,13, \ldots, 30 \).

This implies,

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

Multiples of 7 from 11 to 30 are $14, 21$ and $28$.

Total number of favourable outcomes $=3$.

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 ticket is a multiple of 7 $=\frac{3}{20}$

The probability that the number on the drawn ticket is a multiple of 7 is $\frac{3}{20}$.