What are the odds? DG? Little help?

[Berkut]

So I am playing the new Battles for Normandy game. part of the landing process is to drop your naval support units into place to provide NGF support.

I just put down ten naval units. Each unit rolls 1 1d10 to see if it hits a mine and is removed from the game.

Rolled 5 10s out of the ten dice.

What are the odds of rolling x 10s on ten d10 dice?

I know is is not as simple as one would think, but is there a formula to figure out just how unlikely this result would be?

An "average" roll is obviously 1, but how do you figure how much more unlikely 2 is than 1, 3 than 1, 4, than 1, etc?

[Habbaku]

[Tamas]

Err, we learned this in college it can't be that hard... altough I dont remember much of it : (

[frunk]

If X is the number of 10s:

((9/10)^(10-X)) * ((1/10)^X) * (10!/(X!*(10-X)!))

0: .349
1: .387
2: .194
3: .057
4: .011
5: .001

[Tamas]

  0.1%

[frunk]

Generalizing, if X is the number of desired results, P is the decimal probability of getting the result and N is the number of attempts:

(1-P)^(N-X) * P^X * N! / (X! * (N-X)!)

[Berkut]

0.1%

[The Brain]

It is unlikely that very unlikely events occur.

[Grey Fox]

What's "!" ?

[frunk]

Factorial.  3! is 3*2*1.  10! is 10*9*8*7*6*5*4*3*2*1

[Grey Fox]

Alright, thanks.

[ulmont]

If X is the number of 10s:

((9/10)^(10-X)) * ((1/10)^X) * (10!/(X!*(10-X)!))

0: .349
1: .387
2: .194
3: .057
4: .011
5: .001

You don't need all of that effort since the probabilities aren't unconnected.  To get 5 out of 5, he had to roll every die a 10, meaning it's just (10%) * (10%) * (10%) * (10%) * (10%).  Still .001% though.

[Berkut]

But we are not talking about 5/5, but 5/10.

[frunk]

You don't need all of that effort since the probabilities aren't unconnected.  To get 5 out of 5, he had to roll every die a 10, meaning it's just (10%) * (10%) * (10%) * (10%) * (10%).  Still .001% though.

He's not talking about 5 dice rolling 10s, he's talking about 10 dice, with 5 of them coming up 10s.  If it was 5 dice needing all 10s you'd be right.  Note that my numbers are decimal, not percentage, so 0.1% for rolling 10 dice and 5 of them coming up 10s.

[ulmont]

But we are not talking about 5/5, but 5/10.

Ah, I'm sorry.  I thought you were whining about getting diced, not just having a weird streak.