Question

When you have two dice rolling at the same time, find the following probabilities with proper explanations.

(1) When you will observe a total of 8

(2) When you will observe a total of 4 or a total of 6

(3) When you will observe at least a total of 2

Answer 1

The two dice are rolling at the same time. Hence the sample space 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) }

The total outcomes are = 36

1) The total of 8 :

The possible outcomes are :

{ (2,6),(3,5), (4,4), (5,3), (6,2) }

Hence here number of possible outcomes are 5.

Hence the required probability is,

2) Total of 4 or total of 6.

Possible outcomes of having total 4 is

{ (1,3), ( 2,2 ) , (3,1) }

Number of possible outcomes are 3.

Possible outcomes of having total 6 is

{ (1,5), ( 2,4 ) , (3,3),(4,2), (5,1)  }

Number of possible outcomes are 5.

Hence the required probability is,

= 0.08 + 0.14

= 0.22

3) At least total of 2 .

Here we can see that smallest total is 2 for outcome (1,1) . Hence all other outcomes have total greater than 2.

Hence possible outcomes which have total at least 2 are 36.

Hence the required probability is,