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 $1$?
A) ${\displaystyle \frac{1}{7}}$ B) ${\displaystyle \frac{2}{7}}$ C) ${\displaystyle \frac{3}{7}}$ D) ${\displaystyle \frac{4}{7}}$

Answer 1

Hint: Only the square of numbers $1,0\text{ and - 1}$ will be less than or equal to 1.So the favourable outcomes are 3 out of 7 total outcomes.

Complete step-by-step answer:
Given, total numbers=$\left\{-3,-2,-1,0,1,2,3\right\}$ Then total number of outcomes(n) are $7$ .The squares of these numbers =$\left\{9,4,1,0,1,4,9\right\}$.Now we have to find the probability of choosing the number whose square will be less than or equal to zero. Let the event of choosing the number whose square is less than or equal to one be E then E$=\left\{-1,0,1\right\}=3$ favourable outcomes because only the squares of $1,0\text{ and - 1}$ will be less than or equal to one.
Then , then probability P(E)=${\displaystyle \frac{\text{E}}{\text{n}}}$
 On putting the values we get,
P(E)$={\displaystyle \frac{3}{7}}$
Hence the correct answer is ‘C’.

Note: Here the formula of probability is used which is-
$\Rightarrow \text{Probability = }{\displaystyle \frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}}$ .
The set of all possible outcomes is also known as sample space so we can also write the formula as
$\Rightarrow \text{Probability = }{\displaystyle \frac{\text{Number of favourable outcomes}}{\text{Sample space}}}$