probability formula for group skills checks?

[bms]

Hi, looking for a stats master here.

I have a grid in Excel of all my PCs skills, and I extrapolated that into 3 grids, listing their % likelihood of accomplishing an Easy, Avg or Hard skill check.

What I would like to know is how do I compute the probability of at least 3 of the 5 characters succeeding at a given check.

I'm a bit hazy on independent probabilities, I think I would basically have to calculate the probability of each possible success scenario (a+b+c succeed, a+c+d, a+d+e, b+c+d, b+d+e, etc etc), and add them all up. That's a lot! There must be an Excel function to help with this.

If you care to actually show me, the grid is like this:

___A__B__C___D__E__
1|pc1 pc2 pc3 pc4 pc5
2|.25 .33 .89 .65 .77

Any suggestions?

thanks,
Mike
PS: is there a way to search the forums directly? I tried a google domain search on enworld.org with lots of probability hits, but all of them were about the broken skill challenge system in its various incarnations.

 

[Dr_Ruminahui]

I'm no stats master, but something to keep in mind is how group skill checks affect different party sizes. Basically, even numbered groups have a better chance of passing than odd numbered groups, with the difference between even & odd decreasing the larger the group size.

For example, if you require 50% to pass its a lot easier for a group of 4 (only 2 of 4 need to pass - 50%) than for a group of 3 (2 of 3 need to pass - 67%) or 5 (3 of 5 need to pass - 60%).

 

[bms]

Hi, thanks for chipping in. I agree, party of 4 vs 5 is a big deal. That's one of the reasons I really want to know what the overall probability of success is for any given skill check I might demand.

In my case, I have a group of 5, so I'm focused on "3 or more successes".