Posted by **Dylan** on Tuesday, September 11, 2012 at 11:44pm.

Three fair dice are rolled, and all outcomes are equally likely. What is the probability that the sum of all the numbers on the dice is at most 6?

- Math -
**Steve**, Wednesday, September 12, 2012 at 11:25am
If you count the dice as unique,

there are 6^3 = 216 possible outcomes

There are 42 where the sum is at most 6.

p(sum <= 6) = 42/216 = 7/36

1 1 1

1 1 2

1 1 3

1 1 4 and permutations: 24

1 2 2

1 2 3 and permutations: 12

2 2 2 and permutations: 6

If the dice are indistinguishable, then

there are 56 outcomes

there are 6 where sum <= 6

p(sum <= 6) = 6/56 = 3/28

## Answer this Question

## Related Questions

- Math - Three fair dice are rolled, and all outcomes are equally likely. What is ...
- Probability - When two fair six-sided dice are rolled, there are 36 possible ...
- math - this is real hard and i would love some help. In a game of craps, a ...
- Math - Suppose you play a game in which two fair standard dice are rolled. If ...
- Math Probability - Find the (theoretical) probability of a given event, assuming...
- algebra - two dice are rolled. if a 3 appears on either dice,then the two dice ...
- Mathematics - When two balanced dice are rolled, 36 equally likely outcomes are ...
- math - two 6 sided dice are rolled.what is the probability the sum of the 2 ...
- Math 141 - A pair of fair 6-sided dice is rolled. What is the probability that a...
- math - two dice are rolled find the probability of getting a 5 on either dice or...