# The probability of guessing the correct answer to a question is $\left( {\dfrac{x}{2}} \right)$. If the probability of not guessing the correct answer to this question is $\dfrac{2}{3}$, then x equals:

(A) $2$

(B) $3$

(C) $\dfrac{2}{3}$

(D) $\dfrac{1}{3}$

Last updated date: 22nd Mar 2023

•

Total views: 205.5k

•

Views today: 4.85k

Answer

Verified

205.5k+ views

**Hint:**The given question revolves around the concepts and principles of probability. One must know the basics of probability before attempting the given problem. Simplification rules and transposition are of great significance in solving such type of questions.

**Complete step by step solution:**

In the problem, we are given that the probability of not guessing the correct answer to a question is $\dfrac{2}{3}$.

Also, we are given that the probability of guessing the correct answer to a question is $\left( {\dfrac{x}{2}} \right)$.

Now, we know that the sum of the probabilities in a probability distribution table consisting of all possible ways of doing a certain thing is one. Hence, the sum of probability of happening and not happening of a certain thing is one.

Hence, the sum of probabilities of guessing the correct answer to a question and not guessing the correct answer to a question is one.

Let $P\left( {correct} \right)$ denote the probability of guessing the correct answer and $P\left( {not\,correct} \right)$ denote the probability of not guessing the correct answer.

So, we get, $P\left( {correct} \right) + P\left( {not\,correct} \right) = 1$

Now, we have $P\left( {correct} \right) = \left( {\dfrac{x}{2}} \right)$ and $P\left( {not\,correct} \right) = \dfrac{2}{3}$.

So, substituting the values of probabilities in the equation, we get,

$ \Rightarrow \dfrac{x}{2} + \dfrac{2}{3} = 1$

Now, we have to find the value of x from the above equation.

So, shifting all the constant terms to the right side of equation, we get,

$ \Rightarrow \dfrac{x}{2} = 1 - \dfrac{2}{3}$

Simplifying the expression further, we get,

$ \Rightarrow \dfrac{x}{2} = \dfrac{1}{3}$

Multiplying both the sides of the equation by $2$ , we get,

$ \Rightarrow x = \dfrac{2}{3}$

**Hence, the value of x is $\dfrac{2}{3}$. So, option (C) is correct.**

**Note:**

Probability is a measure of how likely an event is. The value is expressed from zero to one. The sum of all possible probabilities is always one. There are many ways of solving equation as the one formed in the question itself. Method of transposition involves doing the exact same thing on both sides of an equation with the aim of bringing like terms together and isolating the variable or the unknown term in order to simplify the equation and finding the value of the required parameter.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths 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

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE