Calculate the probability of rolling a sum of 3 on two dice and then rolling a sum of 5 on the next roll?

Question

Calculate the probability of rolling a sum of 3 on two dice and then rolling a sum of 5 on the next roll.

Answer 1

For the roll of two dice, the sums can be:

   Sum       ways to get it

     2                    1

     3                    2         [1-2, 2-1]

     4                    3

     5                    4         [1-4, 2-3, 3-2, 4-1]

     6                    5

     7                    6

     8                    5

     9                    4

    10                   3

    11                   2

    12                   1

                      ------

       Total          36

 

So, on two rolls there are 36*36 = 1296 total outcomes and 2*4=8 successful outcomes.

 

[1-2],  [1-4]

[1-2],  [2-3]

[1-2],  [3-2]

[1-2],  [4-1]

[2-1],  [1-4]

[2-1],  [2-3]

[2-1],  [3-2]

[2-1],  [4-1]

 

The probability [  (successful outcomes)/(total outcomes) ] is 8/1296 = 1/162.

Answer 2

With 2 dice there are 36 possibilities to get a number

 

To get a  a sum of 3

There are two ways to get that

 

First  a 1 and a 2 or a 2 and a 1

 

The probability of any number on a dice is 1/6

 

Therefore P(1n2)=1/6^2 and P(2n1) = 1/6^2=2/36=1/18

 

 

To get a sum of 5

 

First  a 1 and a 4, 2 and 3

Then 4 and a 1,then a 3 and 2

 

There are 36 possibilities

 

4/36=1/9