# Dice probability with 2 dice

I am needing an answer put in very simple terms so I can then explain to my son hiw to get to said answer!! The question ;What is the probability of rolling a double six if you threw 2 dice 60 times? Im not bothered about 'fair' dice etc, just normal 6 sided dice! I get that there are 36 possible outcomes per roll of two dice. So over 60 rolls there is 2160 possible outcomes. The question is written in the test just as I have written it above. It doesnt allude to simplfying or converting to percentages etc. All the help you can give would be fantastic thanks

• It is easier to get the complement...that is, the probability that you never get two sixes. On a single roll, that is $\frac {35}{36}$ so the probability that you never get two sixes in $60$ trials is $\left( \frac {35}{36}\right)^{60}$. The answer you want is just $1$ minus that. – lulu Mar 4 '17 at 17:12
• Is it rolling exactly or at least once a double six? I'd guess the latter, and in this case lulu's answer applies. – mlc Mar 4 '17 at 17:13
• Lulu's answer is the definitive answer if the question is about getting two sixes at least once, but if your son is young, you may find that it helps to start with the similar problem of finding the probability of rolling one six when throwing one die a small number of times (one, then two, then three, then generalize). Of course, the formula for one die is $1 - \left(\frac{5}{6}\right)^n$, where $n$ is the number of rolls. You can have your son run experiments, collect data, draw graphs... – Fabio Somenzi Mar 4 '17 at 17:35
• BTW, the number of outcomes is $36^{60}$, which is a much bigger number than $36 \cdot 60 = 2160$. You do care about fair dice, because loaded dice are harder to study. You also want dice that have no "memory." If you rolled dice made of dough, which change shape every time you roll them, they would be much harder to study. – Fabio Somenzi Mar 4 '17 at 17:42

Probability of this question = $1/36+1/36*35/36+1/36*35/6*35/36+...........+1/36*{35/36}^{59} =1/36 \frac{1-\frac{35}{36}^{60}}{1/36} =1-\frac{35}{36}^{60}$