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
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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.
Why do you presume it's random?
Free to try and find a game, dealing cards for sorrow, cards for pain.
I tried having fun once. It was awful.
The random assumption was based on the googling I did regarding what demons guldan returns.
https://us.battle.net/forums/en/hearthstone/topic/20760686734
I admit defeat :P
Legend with : S65 Freeze Mage, S57 Maly Gonk Druid, S57 "Okay" Shaman, S53 Boom-zooka Hunter, S53 Maly Tog Druid, S52 Wild Tog Druid ft.Blingtron, S50 Quest Rogue, S49 Dead Man's Warrior, S41 Wild Clown Fiesta Druid, S41 Hadronox Jade Druid, S40 Wild OTK Dragon Druid, S35 SMOrc Shaman, S33 Jade Druid, S22 Control Priest, S19 Control Priest
We can go with the combinatoric approach:
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.
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:
abcde / abcdf / abcdg / abceg / abcef /abcfg / abefg / abdef / abdfg / abdeg / acdef / acefg
bcdef / bcdfg / bcefg / bdefg / cdefg / adefg / bcdeg / bgcde / cdeag