Question

Two fair six-sided dice are rolled. What is the probability that the sum of the numbers rolled is either 6 or 12? 136+136=236 536+112=29 536+136=16 16+136=736

Answer 1

`(7)/(36)`

Explanation:

Two dices are rolled so total number of sample space =6×6=36

sample space

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

(2,1) (22) (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)

The event which has sum 6, (1,5) (2,4) (3,3) (4,2) (5,1)

So the required probability
`=(6)/(36)=(1)/(6)`

The event which has sum 12 , (6,6)

So the required probability =
`(1)/(36)`

So the total probability =
`(1)/(36)+(1)/(6)=(7)/(6)`