Question

samantha plays a game in which she rolls two standard dice and finds the sum of the dots facing up. which list shows all the possible outcomes for each roll of the dice

Answer 1

List of all possible outcomes is

S = {(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)}

Explanation:

Here Event E = Two dices are rolled at a time

Now here according to the question,

The possible out comes for dice 1, when rolled is: {1,2,3,4,5,6}

The possible out comes for dice 2, when rolled is: {1,2,3,4,5,6}

If both dices are rolled simultaneously, then the sample space S is given as

S = {(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)}

⇒ There are total 36 OUTCOMES when both dices are rolled together.

Now, here sum of both the terms appearing on dice can be

{2,3,4,5,67,8,9,10,11,12}

If the outcomes is: (1,1)} , then SUM OF TERMS is 2.

If the outcomes is: (1,2),(2,1) } , then SUM OF TERMS is 3.

Similarly, If the outcomes is: (6,5),(5,6) } , then SUM OF TERMS is 11.

If the outcomes is: (6,6)} , then SUM OF TERMS is 12.