# Basic probability with dice

This is probably (...) a very basic probability question, but I'd like to be sure about it.

I have 6-sided dice. When rolled, I count one success per dice if the number on the dice is 5 or more.

for each dice, I have a probability of 1/3, but what's the probability of having at least 1 success when rolling n dice at a time?

• This is a generalization of the question asked at stats.stackexchange.com/questions/53154, which is directed at the cases $n=1$ and $n=2$. One of the answers gives a formula for all $n$ and any types of dice (not just six-sided): see "Solution 2" at stats.stackexchange.com/a/53160. – whuber Jan 15 '15 at 20:19
• The usual trick on "at least one success" type problems is to work out the probability of the complementary event ("no successes"), which is usually simple enough to write down immediately. – Glen_b Jan 16 '15 at 1:21

You are describing the binomial distribution. The binomial distribution specifies the probabilities of $x$ number of successes in $n$ independent trials each with probability of success $p$. In your case, $x=1$ and $p=1/3$.
• $P(X >= 1) = 1 - P(X=0) = 1 - (1-p)^n$; I highly recommend the Khan Academy video. – TrynnaDoStat Jan 15 '15 at 19:37