Question

If an integer is chosen at random and squared, then the probability that the last digit of the square is either $1$ or $5,$ is

• A. $\frac{3}{10}$
• B. $\frac{2}{5}$
• C. $\frac{1}{5}$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $\frac{3}{10}$

Last digit of any integer can be $0,1,2,3,4,5,6,7,8,9$
$\therefore n\left(S\right)=10$
Let $A$ be the event that the last digit of square is either $1$ or $5.$
It will be $1$ or $5$ only when the last digit of integer is $1,5$ or $9.$
$\therefore n\left(A\right)=3$
$\Rightarrow P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{3}{10}$