Question

If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll? 25/36 125/216 91/216 11/36 36/216

Answer 1

`(91)/(216)`

Explanation:

1. you know that a dice has 6 sides, and 3 appears once on this dice...

if you roll the dice once, the probability that 3 will happen is
`(1)/(6)`

2. now solving the probability that a 3 will not occur... (this is so we can solve this problem "backwards")

`(5)/(6) * (5)/(6) * (5)/(6)`
`=(125)/(216)`

-
`216` is the total number of possible rolls

-
`125` is the possible rolls that are not 3

3. now that we know the total and the probability that a 3 will not occur...

we can now solve then a 3 will occur!

`216 - 125 = 91`

`(91)/(216)` is the probability the 3 will be rolled!

:D