Question

You are rolling a pair of dice what's is the probability of getting different numbers on both dice

Answer 1

`Pr = 0.833`

Explanation:

Given

A roll of a pair of dice

Required

The probability of getting different numbers

First, list out the sample space;

We have:

`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 is:

`Total = 36`

The outcomes of the different numbers are:

`Different = \{(1, 2) (1, 3) (1, 4) (1, 5) (1, 6),(2, 1) (2, 3) (2, 4) (2, 5) (2, 6),`

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

`(5, 1) (5, 2) (5, 3) (5, 4) (5, 6), (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) \}`

The total is:

`Different = 30`

So, the probability of having a different outcome is:

`Pr = (Different)/(Total)`

`Pr = (30)/(36)`

`Pr = 0.833`