"Question for the math guys!" Topic

Hi.
I was wondering what the percentage chance of rolling at least two "1s" on three dice?

Thanks!

Rob

.074 %

There are 16 combinations that result in either 2 or 3 1's being rolled out of 216 possible combinations.

I brute forced it: went into Excel, wrote out the dice combinations:
1 1 1
1 1 2
1 1 3
etc

Then looked for lines where there are 2 or 3 1's.
I'm sure are more elegant ways to figure it out, but that's my answer. What did I win?

That'd be 7.4% :)
16 combos is right though.
1,1,1.
There are three places where another number can be and 5 numbers other than 1, so 15 other combos with two ones.

There are 6X6X6 or 216 possible combinations of 3 d6. A combination of 1, 1, 1 is therefore only 1 of the possible specific combinations (that it is 1, 1, 1 is only relevant in that there is no ordinal importance to the result, thus making it only 1 possible result).

Therefore the odds are simply 1/216, or approx 0.46%.

One can also calculate the odds by multiplying the odds of each separate die result, which for each is of course 1 in 6, or 16.66… percent.
16.66… cubed (multiplied by itself 3 times) is approx 0.46%.

EDIT: Corrected— forgot to account for the percentage! *face palm*

A combination of 1, 1, 1 is therefore only 1 of the possible specific combinations (that it is 1, 1, 1 is only relevant in that there is no ordinal importance to the result, thus making it only 1 possible result).

Except the OP asked for at least 2 1s on any of the 3 dice, not 3 1s.

The chance of rolling a 1 on a D6 is 1/6.
The chance of not rolling a 1 (ie 2-6) on a D6 is 5/6.

There is only one possible combination of all three 1s, so 1/6 x 1/6 x 1/6 = 1/216.

If you label the dice as A, B, and C, in order to roll two 1s only, then the combinations would be:
A1, B1, C2-6 so 1/6 x 1/6 x 5/6 = 5/216
A1, B2-6, C1 so 1/6 x 5/6 x 1/6 = 5/216
A2-6, B1, C1 so 5/6 x 1/6 x 1/6 = 5/216

So chance of rolling at least two 1s is 1/216 + 3 x 5/216 = 16/216 (7.4%).

That'd be 7.4% :)

{mumble / grumble} stupid percent sign {mumble / grumble}

Thanks for the catch. :)

Ah, missed that detail of 2 out of 3… mea culpa!

1,1,1.
1,1,2. 1,1,3. 1,1,4. 1,1,5. 1,1,6
1,2,1. 1, 3,1. 1,4,1. 1,5,1. 1,6,1
2,1,1. 3,1,1. 4,1,1. 5,1,1. 6,1,1

Those are the combinations for your parameters. Looks like 16 valid rolls.

Dice probability makes a great science fair project. My son took his in middle school and won at the regional competition a few years ago.

You guys are the best! Thanks!

Rob