# Thread: Simple Statistics problem, just need verification.

1. ## Simple Statistics problem, just need verification.

Ok, so I was playing a dice game with my brother, and he had 3 dice.

On 1 roll he rolled three 1s, and on the next roll three 4s.

I did some quick calculations in my head, and I got the probability of that happening as 1 in 46656... Then realised I may be completely off the mark.

My mental calculations took the root $6^3$x $6^3$, or $216$x $216$... I got this because each dice has a 1 in 6 chance of being a certain number (1 through 6), and there were 3 dice each time. I then multiplied the $6^3$s together (obviously also known as $6^6$) to get, after a little thought, 46,656.

This just seems wrong for some reason, please correct me or verify that my reasoning is correct

((Yes, statistics is my weak point, and I'm only 15 anyway ))

((Also feel free to be as complicated as you like in any replies, I'm not stupid ))

2. Originally Posted by BertieWheen
Ok, so I was playing a dice game with my brother, and he had 3 dice.

On 1 roll he rolled three 1s, and on the next roll three 4s.

I did some quick calculations in my head, and I got the probability of that happening as 1 in 46656... Then realised I may be completely off the mark.

My mental calculations took the root $6^3x6^3$, or $216x216$... I got this because each dice has a 1 in 6 chance of being a certain number (1 through 6), and there were 3 dice each time. I then multiplied the $6^3$s together (obviously also known as $6^6$) to get, after a little thought, 46,656.

This just seems wrong for some reason, please correct me or verify that my reasoning is correct

((Yes, statistics is my weak point, and I'm only 15 anyway ))

((Also feel free to be as complicated as you like in any replies, I'm not stupid ))
The probability of rolling three of anything with three rolls is p = (1/6)^3. Therefore the required probability is p^2 and you can check whether this gives the same number that you got.

3. Originally Posted by mr fantastic
The probability of rolling three of anything with three rolls is p = (1/6)^3. Therefore the required probability is p^2 and you can check whether this gives the same number that you got.
I'll see if I can do this without having to go find my calculator

To simplify the (1/6)^3, I assume I just have to know 6^3 which is 216, and therefore (1/6)^3 = 1/216

So p = 1/216 and to find the final probability I simply need to do p^2 which is (1/216)^2 = 1/46656 or 1 in 46,656.

YAY. Thank you ^_^