# From a class of 12 girls and 18 boys, two students are chosen randomly. What is the probability that both of them are girls?

$

{\text{A}}{\text{. }}\dfrac{{22}}{{145}} \\

{\text{B}}{\text{. }}\dfrac{{13}}{{15}} \\

{\text{C}}{\text{. }}\dfrac{1}{{18}} \\

{\text{D}}{\text{. }}\dfrac{1}{{15}} \\

$

Answer

Verified

363.3k+ views

Hint- In this question we have to find the probability that when two students are chosen randomly both of them are girls. So, to solve this we will use combinations and formulas for probability to reach the answer.

We have been given that there are 12 girls and 18 boys in the class. So, there are 30 students in the class in total.

Let A be the event that both of the selected students are girls.

So, $n\left( A \right) = {}^{12}{C_2}$ as we have to select 2 girls out of 12 girls of the class.

Now, let S be the event of selecting two students from the class that is the sample space.

So, $n\left( S \right) = {}^{30}{C_2}$ as we have to select 2 students out of 30 students in the class.

Now, we have the number of favourable outcomes, that is n(A) and the sample space, that is n(S).

So, using the formula of probability we get,

${\text{Probability}} = \dfrac{{n\left( A \right)}}{{n\left( S \right)}}$

So,

${\text{Probability}} = \dfrac{{{}^{12}{C_2}}}{{{}^{30}{C_2}}} = \dfrac{{12!}}{{2! \times \left( {12 - 2} \right)!}} \times \dfrac{{2! \times \left( {30 - 2} \right)!}}{{30!}}$

$ \Rightarrow {\text{Probability}} = \dfrac{{12 \times 11}}{{30 \times 29}} = \dfrac{{22}}{{145}}$

Hence, the correct answer is A. $\dfrac{{22}}{{145}}$

Note- Whenever we face such types of problems the key point to remember is that we need to have a good grasp over probability and combinations. In these types of questions, we should always use combinations to compute the number of favourable outcomes and the sample space as it reduces the probability to make an error to solve the question.

__Complete step-by-step answer:__We have been given that there are 12 girls and 18 boys in the class. So, there are 30 students in the class in total.

Let A be the event that both of the selected students are girls.

So, $n\left( A \right) = {}^{12}{C_2}$ as we have to select 2 girls out of 12 girls of the class.

Now, let S be the event of selecting two students from the class that is the sample space.

So, $n\left( S \right) = {}^{30}{C_2}$ as we have to select 2 students out of 30 students in the class.

Now, we have the number of favourable outcomes, that is n(A) and the sample space, that is n(S).

So, using the formula of probability we get,

${\text{Probability}} = \dfrac{{n\left( A \right)}}{{n\left( S \right)}}$

So,

${\text{Probability}} = \dfrac{{{}^{12}{C_2}}}{{{}^{30}{C_2}}} = \dfrac{{12!}}{{2! \times \left( {12 - 2} \right)!}} \times \dfrac{{2! \times \left( {30 - 2} \right)!}}{{30!}}$

$ \Rightarrow {\text{Probability}} = \dfrac{{12 \times 11}}{{30 \times 29}} = \dfrac{{22}}{{145}}$

Hence, the correct answer is A. $\dfrac{{22}}{{145}}$

Note- Whenever we face such types of problems the key point to remember is that we need to have a good grasp over probability and combinations. In these types of questions, we should always use combinations to compute the number of favourable outcomes and the sample space as it reduces the probability to make an error to solve the question.

Last updated date: 27th Sep 2023

â€¢

Total views: 363.3k

â€¢

Views today: 8.63k

Recently Updated Pages

What is the Full Form of DNA and RNA

What are the Difference Between Acute and Chronic Disease

Difference Between Communicable and Non-Communicable

What is Nutrition Explain Diff Type of Nutrition ?

What is the Function of Digestive Enzymes

What is the Full Form of 1.DPT 2.DDT 3.BCG

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

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

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

One cusec is equal to how many liters class 8 maths CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

Give 10 examples for herbs , shrubs , climbers , creepers

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