Two fair dice are rolled. What is the probability of getting a sum of 7?
$
{\text{A}}{\text{. }}\dfrac{1}{{36}} \\
{\text{B}}{\text{. }}\dfrac{1}{6} \\
{\text{C}}{\text{. }}\dfrac{7}{{12}} \\
{\text{D}}{\text{. }}\dfrac{5}{{12}} \\
$
Last updated date: 27th Mar 2023
•
Total views: 305.7k
•
Views today: 8.86k
Answer
305.7k+ views
Hint: In this question two dice are rolled twice and we need to find the probability of getting a sum 7 so check the total number of outcomes and the favorable number of outcomes of getting a sum 7. Then using the basic definition of probability, we can find the result.
“Complete step-by-step answer:”
According to the theory of probability,
Probability of an event (P) = $\dfrac{{{\text{number of favorable outcomes}}}}{{{\text{Total number of possible outcomes}}}}$
Each roll of a dice has six outcomes (1, 2 … 6).
So, if two dice are rolled simultaneously the total number of outcomes will be
6 x 6 = 36 outcomes.
They are,
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6).
Our Favorable outcomes are = Sum of the numbers on two dice is = 7.
Now, from the above list pick the pairs of numbers whose sum is 7
i.e. (1, 6) (6, 1) (2, 5) (5, 2) (3, 4) (4, 3)
Total favorable outcomes = 6
∴Probability of getting sum 7(P) = $
\dfrac{6}{{36}} \\
\\
$ = $\dfrac{1}{6}$
Note: In order to solve these types of questions, the key point is to look for the perfect formula that evaluates the given data and proceed accordingly. Counting the total possible outcomes and total favorable outcome is crucial, one has to take all possibilities into consideration and be careful about the calculation.
Definition – Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed between zero and one.
“Complete step-by-step answer:”
According to the theory of probability,
Probability of an event (P) = $\dfrac{{{\text{number of favorable outcomes}}}}{{{\text{Total number of possible outcomes}}}}$
Each roll of a dice has six outcomes (1, 2 … 6).
So, if two dice are rolled simultaneously the total number of outcomes will be
6 x 6 = 36 outcomes.
They are,
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6).
Our Favorable outcomes are = Sum of the numbers on two dice is = 7.
Now, from the above list pick the pairs of numbers whose sum is 7
i.e. (1, 6) (6, 1) (2, 5) (5, 2) (3, 4) (4, 3)
Total favorable outcomes = 6
∴Probability of getting sum 7(P) = $
\dfrac{6}{{36}} \\
\\
$ = $\dfrac{1}{6}$
Note: In order to solve these types of questions, the key point is to look for the perfect formula that evaluates the given data and proceed accordingly. Counting the total possible outcomes and total favorable outcome is crucial, one has to take all possibilities into consideration and be careful about the calculation.
Definition – Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed between zero and one.
Recently Updated Pages
If ab and c are unit vectors then left ab2 right+bc2+ca2 class 12 maths JEE_Main

A rod AB of length 4 units moves horizontally when class 11 maths JEE_Main

Evaluate the value of intlimits0pi cos 3xdx A 0 B 1 class 12 maths JEE_Main

Which of the following is correct 1 nleft S cup T right class 10 maths JEE_Main

What is the area of the triangle with vertices Aleft class 11 maths JEE_Main

KCN reacts readily to give a cyanide with A Ethyl alcohol class 12 chemistry JEE_Main

Trending doubts
What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

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

Tropic of Cancer passes through how many states? Name them.

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

Name the Largest and the Smallest Cell in the Human Body ?
