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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.

 Oct 21, 2018

Best Answer 

 #1
avatar+4402 
+2

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

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 Oct 21, 2018
 #1
avatar+4402 
+2
Best Answer

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

Rom Oct 21, 2018
 #2
avatar+99214 
0

Thanks Rom,

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

Melody  Oct 21, 2018

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