Answer:
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)}
Step-by-step 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.
