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

Step-by-step 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: