I swear I leaned this in school at some point but its been bothering me .
If you throw a six sided die, the odds of rolling a six are 1/6.
But what are the odds of rolling at least one six if you throw two dice at the same time? I thought it was 1/6 + 1/6 or 2/6, but suspect I might be wrong.
This is the idea that has me stuck. If you throw 6 dice at the same time what are the odds of rolling at least one 6 ? It can’t be 6/6 or 100%. The odds of rolling at least one 6 are certainly high but absolutely not 100%, so the logic I used for the two dice can’t be correct. There must be a formula for this but I’m having trouble searching for it . Thanks !
In: 12
The logic for 2 dice is as follows. When you roll 2 dice, lets say the first once lands on 1, there are 6 possibilities for the second die. That is also true for all 6 possibilities of the first die. You can get 1,1 1,2 1,3 1,4 1,5 1,6 2,1 2,2…. 6,4 6,5 6,6 or 36 possible pairs.
Now we just count all the pairs that contain a 6
We get 1,6 2,6 3,6 4,6 5,6 6,6
There is also 6,1 6,2 6,3 6,4 6,5 and we already counted 6,6 for a total of 11 of 36 possibilities or a 30.6% chance.
You can also picture a grid.
1 2 3 4 5 6
1 x
2 x
3 x
4 x
5 x
6 x x x x x x
From the visual we can also see a 5×5 grid or 25 pairs that don’t contain a 6 or a 69.4% of no sixes. The same logic can be expanded out for more dice. 5/6 * 5/6 * 5/6… ect which is better than counting pairs.
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