# The probability of solving a problem by three students A , B and C are $\dfrac{1}{2},\dfrac{3}{4}{\text{ and }}\dfrac{1}{4}$

Respectively. The probability that the problem will be solved is

$

{\text{A}}{\text{. }}\dfrac{3}{{32}} \\

{\text{B}}{\text{. }}\dfrac{3}{{16}} \\

{\text{C}}{\text{. }}\dfrac{{29}}{{32}} \\

{\text{D}}{\text{. None of the above}} \\

$

Last updated date: 18th Mar 2023

•

Total views: 304.2k

•

Views today: 4.85k

Answer

Verified

304.2k+ views

Hint: -You have probability of solving problems by students A, B and C is given you have find probability that problem will be solved will be equal to 1- probability of problem can’t be solved.

Complete step-by-step answer:

Given

$P\left( A \right) = \dfrac{1}{2},P\left( B \right) = \dfrac{3}{4},P\left( C \right) = \dfrac{1}{4}$

$

\Rightarrow P\left( {\vec A} \right) = 1 - P\left( A \right) \\

\therefore P\left( {\vec A} \right) = 1 - \dfrac{1}{2} = \dfrac{1}{2} \\

$

$

\Rightarrow P\left( {\vec B} \right) = 1 - P\left( B \right) \\

\Rightarrow P\left( {\vec B} \right) = 1 - \dfrac{3}{4} = \dfrac{1}{4} \\

$

$ \Rightarrow P\left( {\vec C} \right) = 1 - P\left( C \right)$

$\therefore P\left( {\vec C} \right) = 1 - \dfrac{1}{4} = \dfrac{1}{4}$

The probability that problem will be solved = 1- (probability that problem can’t be solved).

$\therefore $Required probability = 1- $P\left( {\vec A \cap \vec B \cap \vec C} \right)$

$\therefore 1 - \dfrac{1}{2} \times \dfrac{1}{4} \times \dfrac{3}{4} = \dfrac{{29}}{{32}}$

Hence option C is the correct option.

Note: -Whenever you get this type of question the key concept of solving is if you have to find probability of success you can write it 1- probability of failure. And you have knowledge of $P\left( {\vec A \cap \vec B \cap \vec C} \right) = P\left( {\vec A} \right) \times P\left( {\vec B} \right) \times P\left( {\vec C} \right)$.

Complete step-by-step answer:

Given

$P\left( A \right) = \dfrac{1}{2},P\left( B \right) = \dfrac{3}{4},P\left( C \right) = \dfrac{1}{4}$

$

\Rightarrow P\left( {\vec A} \right) = 1 - P\left( A \right) \\

\therefore P\left( {\vec A} \right) = 1 - \dfrac{1}{2} = \dfrac{1}{2} \\

$

$

\Rightarrow P\left( {\vec B} \right) = 1 - P\left( B \right) \\

\Rightarrow P\left( {\vec B} \right) = 1 - \dfrac{3}{4} = \dfrac{1}{4} \\

$

$ \Rightarrow P\left( {\vec C} \right) = 1 - P\left( C \right)$

$\therefore P\left( {\vec C} \right) = 1 - \dfrac{1}{4} = \dfrac{1}{4}$

The probability that problem will be solved = 1- (probability that problem can’t be solved).

$\therefore $Required probability = 1- $P\left( {\vec A \cap \vec B \cap \vec C} \right)$

$\therefore 1 - \dfrac{1}{2} \times \dfrac{1}{4} \times \dfrac{3}{4} = \dfrac{{29}}{{32}}$

Hence option C is the correct option.

Note: -Whenever you get this type of question the key concept of solving is if you have to find probability of success you can write it 1- probability of failure. And you have knowledge of $P\left( {\vec A \cap \vec B \cap \vec C} \right) = P\left( {\vec A} \right) \times P\left( {\vec B} \right) \times P\left( {\vec C} \right)$.

Recently Updated Pages

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts

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

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

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE