Question

If you roll two die, what is the likelihood that you will get at least one six?

Answer 1

`P("at least one six on rolling 2 dice") = 11/36`

Explanation:

We can assume without loss of generality that one die is red and the other die is green.

The value that shows up on the red die is not effected by the value that shows up on the green die (i.e. the red and green die faces are independent).

When `A` and `B` are independent
`P(A&B)=P(A)*P(B)`

If `A =` not getting a 6 on the red die
and `B =` not getting a 6 on the green die
Then
`P(A)=5/6` and `P(B) = 5/6`
and
`P("not getting a 6 on either die") = P(A&B) = 5/6*5/6 = 25/36`

`P("getting a 6 on at least one die")`
`color(white)("XXX")=1 - P("not getting a 6 on either die")`

`color(white)("XXX")=1 - 25/36 = 11/36`