Question

A machine generates a two-digit number randomly. Find the probability that the number generated is either less than $25$ or greater than $85.$

• A. $\frac{27}{89}$
• B. $\frac{28}{89}$
• C. $\frac{28}{90}$
• D. $\frac{29}{90}$

Answer 1

The correct option is D $\frac{29}{90}$

Two digit numbers are {$10,11,12,.....98,99$} i.e. $90$ in number.

Number less than 25 ={$10,11,12,13,...,24$} i.e. $15$

Number greater than 85={$86,87,88,....,99$} i.e. $14$

$\therefore$ P(number less than 25 or greater than 85)$=\frac{15}{90}+\frac{14}{90}=\frac{29}{90}$.