Question

A number is chosen at random from the numbers $-3,-2,-1,0,1,2,3$. What will be the probability that the square of this number is less than or equal to $1$?

Answer 1

Given numbers are $-3,-2,-1,0,1,2,3$

Total number of possible outcomes $=7$

The squares of the numbers are given below:

${\left(-3\right)}^2=9,{\left(-2\right)}^2=4,{\left(-1\right)}^2=1,{\left(0\right)}^2=0,{\left(1\right)}^2=1,{\left(2\right)}^2=4,{\left(3\right)}^2=9$

It is clear that the square of $-1,0,1$ is less than or equal to $1$.

Therefore the number of favorable outcomes $=3$

We know that, $\mathrm{Probability}=\frac{\mathrm{number}\mathrm{of}\mathrm{favorable}\mathrm{outcomes}}{\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{possible}\mathrm{outcomes}}$

$=\frac{3}{7}$

Therefore, the probability that the square of the number is less than or equal to $1$is $\frac{3}{7}$.