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How to find probability of one six when a six-sided die is thrown three times ? I tried out the tree diagram but I couldn't get the answer. Please if anyone can help me to solve this problem.

Thank you

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closed as off-topic by John B, user10354138, Henrik, Gibbs, Xander Henderson Nov 4 '18 at 0:06

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  • $\begingroup$ As a hint: since you don't care about the exact value of the non-$6$ outcomes of a single die roll, you can just imagine that there are only two possible outcomes, namely $6$ and $X$ where $X$ just stands for "not $6$". Of course they have different probabilities, namely $\frac 16$ and $ \frac 56$. $\endgroup$ – lulu Nov 3 '18 at 20:36
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    $\begingroup$ When you say one six, I assume you mean exactly one six. This is a binomial distribution with $p = \frac{1}{6}$ and $q = 1 - p = \frac{5}{6}$. $\endgroup$ – Bob Nov 3 '18 at 20:51
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Here is my attempt at a tree. Note, there are $3$ ways to get a single $6$.

enter image description here

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