# An unbiased die is thrown. What is the probability of getting a number greater than 3?

Last updated date: 28th Mar 2023

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Answer

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Hint: This problem can be solved by using the formula of probability in which we need to calculate the number of outcomes possible that satisfy the given conditions and the total number of outcomes possible.

Complete step-by-step answer:

Let us first look into the definitions:

OUTCOME- A possible result of a random experiment is called the outcome.

SAMPLE SPACE- The set of all possible outcomes is called the sample space of an experiment.

EVENT- A subset of the sample space associated with a random experiment is called event.

PROBABILITY- If there are n elementary events associated with a random experiment and m of them are favorable to an event A, then the probability of occurrence of A , denoted by P(A), is given by:

\[P\left( A \right)=\dfrac{m}{n}=\dfrac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}............\left( 1 \right)\]

Given that the die is unbiased which means that there is equal probability for the occurrence of any of the face when a dice is rolled.

That is when a dice is rolled the faces that can be shown are 1,2,3,4,5,6 here by saying that the dice is unbiased means that the probability of showing any one of the 1,2,3,4,5,6 numbers is equal.

Let us assume that rolling of dice is an event named A.

Now here the number of favorable outcomes of getting a number greater than 3 are 3 which are 4, 5, 6.

And the total number of possible outcomes when a dice is rolled are 6 which are 1,2,3,4,5,6.

From the above formula of probability (1) we get,

\[m=3,n=6\]

Now, by substituting these values we can write as:

\[\begin{align}

& \Rightarrow P\left( A \right)=\dfrac{m}{n} \\

& \Rightarrow P\left( A \right)=\dfrac{3}{6} \\

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

\end{align}\]

Hence the probability of getting a number greater than 3 when an unbiased die is rolled is \[\dfrac{1}{2}\].

Note: The condition given in the question about the number greater than 3 is the important part which decides the favorable outcomes of the given event.

Given that the outcome when die is rolled is a number greater than 3. So, we should not consider 3 in the favorable outcomes as it should not be included.

If not an unbiased dice then the probability of occurrence of every number cannot be equal. So, the result changes accordingly if we consider it as biased.

Complete step-by-step answer:

Let us first look into the definitions:

OUTCOME- A possible result of a random experiment is called the outcome.

SAMPLE SPACE- The set of all possible outcomes is called the sample space of an experiment.

EVENT- A subset of the sample space associated with a random experiment is called event.

PROBABILITY- If there are n elementary events associated with a random experiment and m of them are favorable to an event A, then the probability of occurrence of A , denoted by P(A), is given by:

\[P\left( A \right)=\dfrac{m}{n}=\dfrac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}............\left( 1 \right)\]

Given that the die is unbiased which means that there is equal probability for the occurrence of any of the face when a dice is rolled.

That is when a dice is rolled the faces that can be shown are 1,2,3,4,5,6 here by saying that the dice is unbiased means that the probability of showing any one of the 1,2,3,4,5,6 numbers is equal.

Let us assume that rolling of dice is an event named A.

Now here the number of favorable outcomes of getting a number greater than 3 are 3 which are 4, 5, 6.

And the total number of possible outcomes when a dice is rolled are 6 which are 1,2,3,4,5,6.

From the above formula of probability (1) we get,

\[m=3,n=6\]

Now, by substituting these values we can write as:

\[\begin{align}

& \Rightarrow P\left( A \right)=\dfrac{m}{n} \\

& \Rightarrow P\left( A \right)=\dfrac{3}{6} \\

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

\end{align}\]

Hence the probability of getting a number greater than 3 when an unbiased die is rolled is \[\dfrac{1}{2}\].

Note: The condition given in the question about the number greater than 3 is the important part which decides the favorable outcomes of the given event.

Given that the outcome when die is rolled is a number greater than 3. So, we should not consider 3 in the favorable outcomes as it should not be included.

If not an unbiased dice then the probability of occurrence of every number cannot be equal. So, the result changes accordingly if we consider it as biased.

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