Calculating overall percentage/probability from multiple categories?

Spud

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Aug 8, 2018
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Greetings,

My apologies if the title is confusing; I don't really know how to explain what I am trying to do or what label this problem would fall under.

Scenario:
We have a magic bag, and inside the magic bag are an unknown/unlimited amount of coins.
There are 100 different types of coins, but we are only interested in the iron, bronze, silver and gold coins, so we have bundled the other 96 types together as "other".

We performed an experiment by taking one coin at a time from the magic bag and recording what type of coin it was; the coins we took from the magic bag were not placed back into the magic bag.
We performed the experiment 1,000,000 times and the results are as follows:

Other coins: 998,859
Iron coins: 596
Bronze coins: 312
Silver coins: 135
Gold coins: 98


First Question:
Is it correct to say the probability to receive each coin from the magic bag is as follows?

Other coins: (998,859/1,000,000)*100 = 99.8859% or 1,000,000/998,859 = 1 in 1.0011423
Iron coins: (596/1,000,000)*100 = 0.0596% or 1,000,000/596 = 1 in 1,678
Bronze coins: (312/1,000,000)*100 = 0.0312% or 1,000,000/312 = 1 in 3,205
Silver coins: (135/1,000,000)*100 = 0.0135% or 1,000,000/135 = 1 in 7,407
Gold coins: (98/1,000,000)*100 = 0.0098% or 1,000,000/98 = 1 in 10,204


Second Question:
If I take only one coin from the magic bag, what is the chance/probability to receive either an iron, bronze, silver or gold coin?
(Receiving any of these four coins would be a success, and receiving any of the other 96 coins would be a failure).

I have tried to do some calculations, but I don't think I am working it out properly.
- Is the following correct?
((0.0596/100)+(0.0312/100)+(0.0135/100)+(0.0098/100))*100 = 0.1141% (or 100% - 99.8859% = 0.1141%)

- Is the following correct?
((1/1678)+(1/3205)+(1/7407)+(1/10204))*100 = 0.1141%

- Is the following correct?
(((1/1678)+(1/3205)+(1/7407)+(1/10204))/4)*100 = 0.0285%


Third Question:
If I take 1,400 coins from the magic bag, what is the chance/probability to receive either an iron, bronze, silver or gold coin?
(Receiving any of these four coins would be a success, and receiving any of the other 96 coins would be a failure).

I really have no idea how to calculate this; all I have managed to do is repeat one of the formulas above and multiply by 1,400.

- Is the following correct?
((((1/1678)+(1/3205)+(1/7407)+(1/10204))/4)*100)*1400 = 39.9339%


Fourth Question:
What is the name for this type of probability?



I understand that I am probably completely wrong about everything, so thank you very much to anyone willing to provide assistance.
 
You do not say how you conducted this experiment. I presume you mean you programmed some kind of simulation. In that case, how did you sample without replacement? That is easy enough to do in a physical experiment (though it is bad sampling technique), but how did you set it up in a simulation? And why would you do it?

A probability is a number greater than or equal to zero and less than or equal to 1. When you get a probability above 1 you are doing something wrong.

In a random sample with replacement, the proportions that you get from the sample are unbiased estimates of the proportions to be found in the underlying population.
 
You do not say how you conducted this experiment. I presume you mean you programmed some kind of simulation. In that case, how did you sample without replacement? That is easy enough to do in a physical experiment (though it is bad sampling technique), but how did you set it up in a simulation? And why would you do it?

A probability is a number greater than or equal to zero and less than or equal to 1. When you get a probability above 1 you are doing something wrong.

In a random sample with replacement, the proportions that you get from the sample are unbiased estimates of the proportions to be found in the underlying population.


Hi Jeff M,

I must say that my knowledge and experience with probability is extremely minimal, so to be honest I don't really understand your objection; is it not possible to determine the probability of certain outcomes based on the data provided?

I wish to adjust the scenario and perhaps that will make things more clear.

Scenario:
We have a magic bag, and inside the magic bag are an unlimited amount of coins.
We don't know how many types of coins there are, but we are only interested in the iron, bronze, silver and gold coins.
There is a tag attached to the magic bag that states the probability of receiving the following coins:

Iron coins: 0.0596%
Bronze coins: 0.0312%
Silver coins: 0.0135%
Gold coins: 0.0098%

We are not given any other information.

Question 1:
If I take one coin, what is the probability of that one coin being either an iron, bronze, silver or gold coin?
I mean to say that I am putting the iron, bronze, silver and gold coins into a group of preferred coins, and receiving any of them would be a success.

Question 2:
If I take 1,400 coins, what is the probability that among those 1,400 coins, at least one of them is an iron, bronze, silver or gold coin?
I mean to say that I am putting the iron, bronze, silver and gold coins into a group of preferred coins, and receiving at least one of any of them would be a success.


I hope this is more clear; my apologies if it's not.
 
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