A bag contains cards which are numbered from 2 to 90. A card is drawn at random from the bag. Find the probability that it bears a two digit number.

Given:

A bag contains cards which are numbered from 2 to 90. A card is drawn at random from the bag.

To do:

We have to find the probability that it bears a two digit number. 

Solution:

A bag contains cards numbered \( 2,3,4, .., 89,90 \).

This implies,

The total number of possible outcomes $n=89$.

Two digit numbers from 2 to 90 are $10, 11, .........., 89, 90$.

Total number of favourable outcomes $=81$.

We know that,

Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

Therefore,

Probability that the card bears a two digit number $=\frac{81}{89}$

The probability that it bears a two digit number is $\frac{81}{89}$.