Question

A dice is thrown two times and sum of the numvers appearing on the dice are noted.The number of possible outcomes is ​

Answer 1

Only one dice is thrown twice.

The possible outcomes are

The sum of the numbers are noted.

1) If the sum is 2

possible outcome 1 on first thrown and one on second thrown.

2) If the sum is 3

possible out comes  1 on first yime, 2 on second time

or 2 on first time , 1 on second time.

3) If the sum is 4 , possible outcomes:

1 on first time , 3 on second time

3 on first time , 1 on second time

2 on both times.

So If now we consider about total possible outcomes,

when the dice is rolled , It will show any number on both throws , and their sum will also be noted.

So possible outcomes is as same as possible outcomes on throwing a dice two times.

That is

=36

The first one (1,1) is for sum to be=2

The second one (1,2) and 7th one (2,1) is for sum to be equal to 3

The third , eighth and 13th (3,1) is for sum to be equal to 4.

And so on

So possible outcomes are 36