Question

Imagine you have a pair of six-sided dice. What's the

probability of rolling a seven or rolling an even number

as the sum of the two dice?

Answer 1

The probability of rolling a seven or rolling an even number as the sum of the two dice is
`(2)/(3)`

Explanation:

Given : Imagine you have a pair of six-sided dice.

To find : What's the probability of rolling a seven or rolling an even number as the sum of the two dice?

Solution :

Rolling a pair of six-sided dice,

(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)

Rolling a seven as the sum of the two dice are (1,6),(2,5),(3,4),(4,3),(5,2),(6,1)

Rolling an even number as the sum of the two dice are (1,1),(1,3),(1, 5),(2, 2),(2, 4),(2, 6) ,(3, 1),(3, 3),(3, 5),(4, 2),(4, 4),(4, 6),(5, 1),(5, 3),(5, 5),(6, 2),(6, 4),(6, 6).

Favorable outcome of rolling a seven or rolling an even number as the sum of the two dice are (1,6),(2,5),(3,4),(4,3),(5,2),(6,1), (1,1),(1,3),(1, 5),(2, 2),(2, 4),(2, 6) ,(3, 1),(3, 3),(3, 5),(4, 2),(4, 4),(4, 6),(5, 1),(5, 3),(5, 5),(6, 2),(6, 4),(6, 6) - 24

The probability is given by,

`\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total outcome}}`

`\text{Probability}=(24)/(36)`

`\text{Probability}=(2)/(3)`

Therefore, the probability of rolling a seven or rolling an even number as the sum of the two dice is
`(2)/(3)`