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You roll a fair die four times.  What is the probability of getting a 6 at least once?

 Jun 29, 2020
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we can use complementary counting to solve this one!


the only way you can't get a 6 at least once is if you get no sixes in 4 throws.

 

so, if you get no sixes in four throws, there are 5 possibilities for each throw, and therefore \(5^4=625\) possibilities with no six out of the \(6^4=1296\)  possibilities in total.

 

so you get the probability by taking the \(1296-625=671\) possibilities which must include at least one six, out of the \(1296\) possibilities altogether.

 

so the answer is \(\boxed{\dfrac{671}{1296}}\).

 Jun 29, 2020

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