i just won a game and was trying to determine if I got lucky or if the odds were in my favor, but I stink at statistics.
i was playing cubelock andthese 7 demons had already died, 1 voidlord, 3 1/3 demons, and 3 doomguards. I played guldan and had 5 open spots on the board. I needed all three doomguards to come back in order to win, which they did.
What are the odds of this happening? I calculated the odds to be 3/42. That seemed really low to me.
This is how I think to solve this. To summon 5 demons out of 7 dead demons no matter the order has 21 combinations (''7 choose 5''). To summon 3 specific demons to these 5 spots it is 6 combinations. So the overall possibility to summon 3 doomguards or 3 voidwalkers is 6/21 or 29%.
Let's say the demons who died are a b c d e f and g. (Lets suppose that e f g are the doomguards). The possible combinations ( the order is irrelevant) when these demons are resurrected, are the following:
We want to arrange 7 minions in line, a winning scenario is having 3 Doomguard in the first 5 spots.
Total number of arrangements is 7!.
Let's count winning scenarios:
First choose the Doomguard spots: 5 choose 3 = 10
Now, choose where each doomguard will be: 3! = 6
Last, choose where the rest of the demons will be: 4! = 24
So the probability of winning is: (10*6*24)/7! = 1440/5040 = 2/7.
Two matching Results out of so many posts. Math is hard hahaha
Both of you get a gold star for getting the answer correct though. You enumerated the possibilities as well so it is clear that is the correct answer.
I'm a little concerned you used e, f and g as your positive results when I was expecting a, b and c ;) You can just use D and N (for doomguard/not doomguard) as well to make it simpler (max 3 D's though out of the 5 of course).
To OP: This is a question about probability and not statistics - statistics is applied probability :P