Question

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box , find the probability that it bears
A two- digit number

Answer 1

Total number of discs$=90$

Number of two digit numbers in the discs$=10,11,...90$

Since difference between the consecutive numbers is same.

These numbers form an A.P

First number$=a=10$

Common difference$=d=11-10=1$

Last number $=a_n=90$

$a_n=a+(n-1)d$

$\Rightarrow 90=10+(n-1)1$

$\Rightarrow n=90-9=81$

$\therefore$ Total number of two digit numbers between $1$ and $90$ is $81$

So,Total number of discs with two digit numbers $=81$

$P(gettingatwo-digitnumber)=\frac{Totalnumberofdiscwithtwodigitnumber}{totalnumberofdiscs}$

$=\frac{81}{90}=\frac{9}{10}$