Posted by **juan777** on Monday, January 23, 2012 at 12:31am.

A six sided die is rolled three times. List possible outcomes and find the probability of rolling exactly one 6.

- math -
**Reiny**, Monday, January 23, 2012 at 8:52am
Are you sure that they want you to "list" all the outcomes?

There are 216 of them. (6x6x6=216)

If you have to list them, do it systematically, e.g.

1 1 6

1 1 5

...

1 1 1

1 2 6

1 2 5

....

1 2 1

1 3 6

.....

....

1 6 1

...

2 1 6

2 1 5

etc

To have only one 6, it must look like this

6 x y, x 6 y, x y 6, where the x and y are NOT 6

number of those = 3x5x5 = 75

prob (exactly one 6) = 75/216 = 25/72

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