# 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 :

Last updated date: 29th Mar 2023

•

Total views: 309.9k

•

Views today: 2.86k

Answer

Verified

309.9k+ 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

If ab and c are unit vectors then left ab2 right+bc2+ca2 class 12 maths JEE_Main

A rod AB of length 4 units moves horizontally when class 11 maths JEE_Main

Evaluate the value of intlimits0pi cos 3xdx A 0 B 1 class 12 maths JEE_Main

Which of the following is correct 1 nleft S cup T right class 10 maths JEE_Main

What is the area of the triangle with vertices Aleft class 11 maths JEE_Main

KCN reacts readily to give a cyanide with A Ethyl alcohol class 12 chemistry JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?