Question

# Two fair dice are rolled. What is the probability of getting a sum of 7?${\text{A}}{\text{. }}\dfrac{1}{{36}} \\ {\text{B}}{\text{. }}\dfrac{1}{6} \\ {\text{C}}{\text{. }}\dfrac{7}{{12}} \\ {\text{D}}{\text{. }}\dfrac{5}{{12}} \\$

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.

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.