Answer
Verified
455.7k+ views
Hint: We should know that the ratio of favourable outcomes to total number of outcomes is called probability. We know that from a die we get the outcomes are 1, 2, 3, 4, 5 and 6. So, now we have the total number of outcomes. Now we have to calculate the total number of favourable outcomes. Now we have to find a number of outcomes greater than 3. This will give the total number of favourable outcomes. Now we have to find the ratio of the number of favourable outcomes to the total number of outcomes. This will give us the probability that the number will appear to be greater than 3.
Complete step by step answer:
Before solving the question, we should know the definition of probability. The ratio of favourable outcomes to total number of outcomes is called probability. Now by using this definition, we can find the probability.
From the question, it was given that to find out the probability that the number will appear greater than 3. Now we have to find the total number of outcomes from a die and we have to find the total number of favourable outcomes.
From a die, the possible outcomes are \[1,2,3,4,5,6\]. So, the total number of outcomes are equal to 6. We know that the numbers greater than 3 and less than or equal to 6 are 4, 5, 6. So, the total numbers that are greater than 3 are equal to 3. So, the total number of favourable outcomes are equal to 3.
Let us assume the total number of favourable outcomes are equal to m, total number of outcomes are equal to n and the probability is equal to P(A). So, the ratio of m and n is equal to P(A).
\[\begin{align}
& m=3....(1) \\
& n=6....(2) \\
& P(A)=\dfrac{m}{n}....(3) \\
\end{align}\]
Now we will substitute equation (1) and equation (2) in equation (3).
\[\begin{align}
& \Rightarrow P(A)=\dfrac{3}{6} \\
& \Rightarrow P(A)=\dfrac{1}{2}....(4) \\
\end{align}\]
So, from equation (4), it is clear that the probability that the number will appear to be greater than 3 is equal to \[\dfrac{1}{2}\].
Note: Students should be careful while reading the question. Some students may think that it was asked to find the probability of having a number that is greater than or equal to 3. Then we get the number of favourable outcomes is equal to 4. We already know that the number of outcomes is equal to 6.
Let us assume the total number of favourable outcomes are equal to m, total number of outcomes are equal to n and the probability is equal to P(A). So, the ratio of m and n is equal to P(A).
\[\begin{align}
& m=4....(1) \\
& n=6....(2) \\
& P(A)=\dfrac{m}{n}....(3) \\
\end{align}\]
Now we will substitute equation (1) and equation (2) in equation (3).
\[\begin{align}
& \Rightarrow P(A)=\dfrac{4}{6} \\
& \Rightarrow P(A)=\dfrac{2}{3}....(4) \\
\end{align}\]
So, from equation (4), it is clear that the probability that the number will appear to be greater than 3 is equal to \[\dfrac{2}{3}\].
Complete step by step answer:
Before solving the question, we should know the definition of probability. The ratio of favourable outcomes to total number of outcomes is called probability. Now by using this definition, we can find the probability.
From the question, it was given that to find out the probability that the number will appear greater than 3. Now we have to find the total number of outcomes from a die and we have to find the total number of favourable outcomes.
From a die, the possible outcomes are \[1,2,3,4,5,6\]. So, the total number of outcomes are equal to 6. We know that the numbers greater than 3 and less than or equal to 6 are 4, 5, 6. So, the total numbers that are greater than 3 are equal to 3. So, the total number of favourable outcomes are equal to 3.
Let us assume the total number of favourable outcomes are equal to m, total number of outcomes are equal to n and the probability is equal to P(A). So, the ratio of m and n is equal to P(A).
\[\begin{align}
& m=3....(1) \\
& n=6....(2) \\
& P(A)=\dfrac{m}{n}....(3) \\
\end{align}\]
Now we will substitute equation (1) and equation (2) in equation (3).
\[\begin{align}
& \Rightarrow P(A)=\dfrac{3}{6} \\
& \Rightarrow P(A)=\dfrac{1}{2}....(4) \\
\end{align}\]
So, from equation (4), it is clear that the probability that the number will appear to be greater than 3 is equal to \[\dfrac{1}{2}\].
Note: Students should be careful while reading the question. Some students may think that it was asked to find the probability of having a number that is greater than or equal to 3. Then we get the number of favourable outcomes is equal to 4. We already know that the number of outcomes is equal to 6.
Let us assume the total number of favourable outcomes are equal to m, total number of outcomes are equal to n and the probability is equal to P(A). So, the ratio of m and n is equal to P(A).
\[\begin{align}
& m=4....(1) \\
& n=6....(2) \\
& P(A)=\dfrac{m}{n}....(3) \\
\end{align}\]
Now we will substitute equation (1) and equation (2) in equation (3).
\[\begin{align}
& \Rightarrow P(A)=\dfrac{4}{6} \\
& \Rightarrow P(A)=\dfrac{2}{3}....(4) \\
\end{align}\]
So, from equation (4), it is clear that the probability that the number will appear to be greater than 3 is equal to \[\dfrac{2}{3}\].
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE