Question

The faces of an eight-sided solid are labeled 1 through 8. Each

number has an equal chance of being rolled. Two of these solids

are rolled. What is the probability that an odd number is rolled on

both solids?

Answer 1

The probability that an odd number is rolled on both solids is
`(1)/(4)`.

Explanation:

Consider the provided information.

For the 8 sided dice the total number of outcomes = 64.

The favourable outcomes i.e odd numbers on both the solid = 16

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (1,7), (1,8)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (2,7), (2,8)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (3,7), (3,8)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (4,7), (4,8)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (5,7), (5,8)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6), (6,7), (6,8)

(7,1), (7,2), (7,3), (7,4), (7,5), (7,6), (7,7), (7,8)

(8,1), (8,2), (8,3), (8,4), (8,5), (8,6), (8,7), (8,8)

We know that
`\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}`

`\text{Probability of odd on both solid}=(16)/(64)`

`\text{Probability of odd on both solid}=(1)/(4)`

Hence, the probability that an odd number is rolled on both solids is
`(1)/(4)`.