Question

Two fair dice are tossed and the number on each die is recorded, e.g. (3,2) indicates the first die had 3 and the second die had a 2. In total, there are 36 (equally likely) outcomes in the sample space. What is the probability the sum of the two dice is 7

Answer 1

`(1)/(6)`

Explanation:

Given that two fair dice are tossed.

Total outcomes as we toss two dice are given as:

{

(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)

}

Where (a, b) represents a is the outcome of the die rolled for the 1st time and b is the outcome of 2nd toss of the die.

Total number of outcomes = 36

The outcomes with sum = 7 are :

{(1, 6), (2, 5), (3, 4) , (4, 3), (5, 2), (1, 6)}

Number of outcomes = 6

Probability of an event E is given as:

`P(E) = \frac{\text{Number of favorable cases}}{\text {Total number of cases}}`

`P(sum=7) = (6)/(36)\\\Rightarrow \bold{P(sum=7) = (1)/(6)}`