A number $x$ is chosen at random from the set $\{ 1,2,3,4,...........,100\} .$ Define the event:
$A = $ the chosen number $x$ satisfies $\dfrac{{(x - 10)(x - 50)}}{{(x - 30)}} \geqslant 0.$ Then $P(A)$is :
Answer
384.6k+ views
Hint-Wavy curve method defined as the limit of x from the given equation. And probability is the ratio of favorable number of outcomes to the total number of outcomes. With the help of these definitions we will solve the question.
Given that:
$ \Rightarrow \dfrac{{(x - 10)(x - 50)}}{{(x - 30)}} \geqslant 0$
We will use the wavy curve method to find the solution of the above equation.
By wavy curve method, the solution is
$\{ 10,11,12,..........29\} U\{ 50,51,......100\} $
The value of $x = 30$ is neglected because it does not satisfy the above equation, therefore
$
n(A) = 20 + 51 \\
= 71 \\
$
The probability of chosen no satisfies the given equation is
$
P(A) = \dfrac{{n(A)}}{{n(Givenset)}} \\
= \dfrac{{71}}{{100}} = 0.71 \\
$
Hence probability of the event is 0.71
Note- This problem combines the concept of both probability and solutions of polynomial equations. For this problem the sample space is a solution of the polynomial equation which we found using a wavy curve method. In probability problems first we have to define the event and then sample space. After this we proceed further to solve the problem.
Given that:
$ \Rightarrow \dfrac{{(x - 10)(x - 50)}}{{(x - 30)}} \geqslant 0$
We will use the wavy curve method to find the solution of the above equation.

By wavy curve method, the solution is
$\{ 10,11,12,..........29\} U\{ 50,51,......100\} $
The value of $x = 30$ is neglected because it does not satisfy the above equation, therefore
$
n(A) = 20 + 51 \\
= 71 \\
$
The probability of chosen no satisfies the given equation is
$
P(A) = \dfrac{{n(A)}}{{n(Givenset)}} \\
= \dfrac{{71}}{{100}} = 0.71 \\
$
Hence probability of the event is 0.71
Note- This problem combines the concept of both probability and solutions of polynomial equations. For this problem the sample space is a solution of the polynomial equation which we found using a wavy curve method. In probability problems first we have to define the event and then sample space. After this we proceed further to solve the problem.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are

Why should electric field lines never cross each other class 12 physics CBSE

An electrostatic field line is a continuous curve That class 12 physics CBSE

What are the measures one has to take to prevent contracting class 12 biology CBSE

Suggest some methods to assist infertile couples to class 12 biology CBSE

Amniocentesis for sex determination is banned in our class 12 biology CBSE

Trending doubts
Which one of the following places is unlikely to be class 8 physics CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is 1 divided by 0 class 8 maths CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What is pollution? How many types of pollution? Define it

Difference Between Plant Cell and Animal Cell

Find the HCF and LCM of 6 72 and 120 using the prime class 6 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers
