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A 6-sided fair die is rolled 10 times. What is the probability of a third 6 on the 10th roll? Thank you.

Guest Oct 21, 2018

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$P[\text{3rd 6 on roll 10}]=P[\text{2 6's in 9 rolls and a 6 on the 10th roll}=\\ \dbinom{9}{2}\left(\dfrac 1 6\right)^2 \left(\dfrac 5 6\right)^7 \cdot \dfrac 1 6 = \dfrac{78125}{1679616}$

Rom Oct 21, 2018

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Thanks Rom,

I don't think I would have thought to do that.

Melody Oct 21, 2018

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Rom · Answer 1 · 2018-10-21T01:51:59

$P[\text{3rd 6 on roll 10}]=P[\text{2 6's in 9 rolls and a 6 on the 10th roll}=\\ \dbinom{9}{2}\left(\dfrac 1 6\right)^2 \left(\dfrac 5 6\right)^7 \cdot \dfrac 1 6 = \dfrac{78125}{1679616}$

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