Question

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

Answer 1

Answer:

$Pr = 0.833$

Step-by-step 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:

$Pr = \frac{Different}{Total}$

$Pr = \frac{30}{36}$

$Pr = 0.833$