Question

Consider rolling dice and getting a total of 8. Find the probability if two dice are rolled. (Enter the value of probability in decimals. Round the answer to three decimal places.) (You must provide an answer before moving to the next part.)

Answer 1

Answer:

$Pr = \frac{2}{9}$

Step-by-step explanation:

Given

A roll of two dice

Required

Probability of getting a sum of 8

First, we list out the sample space

$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:

$n(S) = 36$

From the sample space, the outcomes that give a sum of 8 are:

$Sum =\{(2, 6), (3, 5),(4,4),(5,3),(6,2)\}$

The total is:

$n(Sum) = 8$

So, the probability is:

$Pr = \frac{n(Sum)}{n(S)}$

$Pr = \frac{8}{36}$

$Pr = \frac{2}{9}$