• Dec 8th 2012, 10:45 AM
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 :-)
• Dec 8th 2012, 11:31 AM
Soroban
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: . $P(\text{sum}\le 5) \;=\;\frac{10}{216} \;=\;\frac{5}{108}$
• Dec 8th 2012, 11:32 AM
Plato
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 $x^3,~x^4,~\&~x^5$.
• Dec 8th 2012, 01:23 PM
HallsofIvy