# Math Help - please help probability question

1. ## please help probability question

Three fair 6 sided dice are rolled. Find the probability that the total on all three dice is 5 or less.?
ans10/216 pleease explain your method :-)

2. ## Re: please help probability question

Hello, aimsywamesy!

Three fair 6-sided dice are rolled.
Find the probability that the total on all three dice is 5 or less.
Ans: 10/216

There are: $6^3 = 216$ possible outcomes.

Outcomes with sums $\le 5$

. . $\begin{array}{c} (1,1,1) \\ (1,1,2)\;(1,2,1)\;(2,1,1) \\ (1,1,3)\;(1,3,1)\;(3,1,1) \\ (1,2,2)\;(2,1,2)\;(2,2,1) \end{array}$ . . 10 outcomes

Therefore: . $P(\text{sum}\le 5) \;=\;\frac{10}{216} \;=\;\frac{5}{108}$

3. ## Re: please help probability question

Originally Posted by aimsywamesy
Three fair 6 sided dice are rolled. Find the probability that the total on all three dice is 5 or less.?
ans10/216 pleease explain your method :-)

There are 216 possible triples.

Make a list of favorable outcomes.
We can get 1,1,1 in one way.
We can get 1,1,2 in three ways: 112, 121, 211.
Same for 113. So far that is seven favorable outcomes.

According to the give answer you should find ten in all.

Or go to this webpage add up the coefficients of $x^3,~x^4,~\&~x^5$.

4. ## Re: please help probability question

"Two great minds with a single thought!"