# please help probability question

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• December 8th 2012, 10:45 AM
aimsywamesy
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 :-)
• December 8th 2012, 11:31 AM
Soroban
Re: please help probability question
Hello, aimsywamesy!

Quote:

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: . $P(\text{sum}\le 5) \;=\;\frac{10}{216} \;=\;\frac{5}{108}$
• December 8th 2012, 11:32 AM
Plato
Re: please help probability question
Quote:

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 $x^3,~x^4,~\&~x^5$.
• December 8th 2012, 01:23 PM
HallsofIvy
Re: please help probability question
"Two great minds with a single thought!"