Probability Three Dice Sum To 18

Suppose three fair six-sided dice are rolled. What is the probability that the sum of the numbers obtained equals 18?

1 36 \dfrac{1}{36} 1 129 \dfrac{1}{129} 1 216 \dfrac{1}{216} 1 1296 \dfrac{1}{1296}

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Lucas Moreno
Mar 20, 2021

To get 18, we would have to get six three consecutive times. The probability of this is 1 over 6 to the third power, which is 1 in 216.

To put that in perspective, suppose you raise a spade card of the 13 on the card deck. The chance of raising twice the same card is 1 in 169, which is a bit more likely than 1 in 216.

Justin Malme
Jun 7, 2016

The only combination that equals 18, is 6+6+6.
There are 6 3 = 216 6^3=216 possible combinations, so 1 216 \frac{1}{216} .

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...