How would you calculate the probability of something without replacement?

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#1

Using the classic Marbles In A Bag example, given a table like this and a set amount of selections, how would you calculate the expected chance of something occurring without replacement? I am trying to calculate the percentage chance of the player being a starter zombie in a zombie game, so that the player can see their chance of being a zombie because it is not a static chance each round.

local SelectionsAmount = 2
local Marbles= {
	["Red"] = 4,
	["Blue"] = 5,
}

A model of what I am trying to calculate:

image
image577×654 20.7 KB

#2

I have solved my own problem, if anyone needs the script here you go. I used placeholder variables for it, but you can change around the numbers in it if you need

--Placeholders
local Exit = {
	["Chad"] = 3,
	["Bob"] = 2,
	["James"] = 2,
	["Hunter"] = 5
}
local ZombieAmount = 1
local ChanceOfZombie = 0
local LocalName = "Hunter"

--Function, do not edit
local ChancesTable = {}
local StartTick = tick()
local function recursion(CurrentTable,HypotheticalZAmount,PrevChance)
	if HypotheticalZAmount < ZombieAmount then
		local TotalAmount = 0
		for PlrName,Amount in pairs(CurrentTable) do
			TotalAmount += Amount
		end
		for Selection,Num in pairs(CurrentTable) do
			local ChanceOfSelection = Num/TotalAmount
			if Selection == LocalName then
				ChanceOfZombie += (Exit[LocalName]/TotalAmount)*PrevChance
			else
				local NewTable = {}
				for PlrName,Amount in pairs(CurrentTable) do
					if PlrName ~= Selection then
						NewTable[PlrName] = Amount
					end
				end
				recursion(NewTable,HypotheticalZAmount+1,ChanceOfSelection)
			end
		end
	end
end

recursion(Exit,0,1)
print(ChanceOfZombie) --This print statement returns the decimal
print(math.floor((ChanceOfZombie*100)+0.5).."%") --This print statement returns String version, useful for UIS