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If you roll a die 5 times, what is the probability that you roll at least one five.

Is it p(1/5), or do I need to do a bionomcdf, I'm confused.

robbin
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  • Related : http://math.stackexchange.com/questions/697433/a-family-has-three-children-what-is-the-probability-that-at-least-one-of-them-i – lab bhattacharjee Mar 15 '14 at 16:42
  • Let $X$ be the number of fives. You want $\Pr(X\ge 1)$. This is $\Pr(X=1)+\Pr(X=2)+\cdots+\Pr(X=5)$. You could calculate them all and add up, using the binomial distribution. For example, $\Pr(X=2)=\binom{5}{2}(1/5)^2(5/6)^3$. However, the procedure used in the current answer is far quicker. – André Nicolas Mar 15 '14 at 17:07
  • If you encounter expressions like 'at least' or 'at most' in the event, then see that as an encouragement to look at the complement of the event. Its probability is (almost) always much easyer to calculate. – drhab Mar 15 '14 at 17:38

1 Answers1

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HINT:

Probability of no five in $5$ rolling is $$\left(\frac56\right)^5$$

Probability of at least one five $=1-$ Probability of no five

lab bhattacharjee
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