Question

If a number $x$ is chosen at random from the numbers $-3,-2,-1,0,1,2,3$ . What is the probability that ${{x}^{2}}\le 4$ ?

Answer 1

Here we have been given some numbers and we have to find the probability of their square to be greater than $4$ . Firstly we will find the square of all the numbers given then we will check how many number squares are less than equal to $4$ . Finally we will find the probability of that happening by dividing the number that satisfies the property by the total number of numbers given and get the desired answer.

Complete step-by-step solution:
The numbers are given as follows:
$-3,-2,-1,0,1,2,3$
We have to find the probability if a number is chosen at random that its square is less than equal to $4$ .
Now we will find the square of all the numbers as follows:
${{\left( -3 \right)}^{2}},{{\left( -2 \right)}^{2}},{{\left( -1 \right)}^{2}},{{\left( 0 \right)}^{2}},{{\left( 1 \right)}^{2}},{{\left( 2 \right)}^{2}},{{\left( 3 \right)}^{2}}$
$\Rightarrow 9,4,1,0,1,4,9$
Now as we can see that five among the seven numbers given square is less than and equal to $4$ .
Total number satisfying the condition $=5$
Total numbers $=7$
So the probability of ${{x}^{2}}\le 4$ happening is as follows:
Probability $=$ Total number satisfying the condition $\div$ Total numbers
Probability $=\dfrac{5}{7}$
Hence if a number $x$ is chosen at random from the numbers $-3,-2,-1,0,1,2,3$ the probability that ${{x}^{2}}\le 4$ is $\dfrac{5}{7}$.

Note: Probability is an important branch of mathematics that deals with how likely an event is to occur or how likely the proposition is true. The value of probability always lies between $0\And 1$ . Where $0$ means it is impossible that the event will occur and $1$ means that the event will definitely occur. In this type of question the first thing is to use the operation given and then check which among them satisfy the value given.