Help with Probilities

Zetaphax

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Aug 22, 2014
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I am currently looking for a formula and after an hour and a half of searching the web decided to just ask a math forum. I have no idea what this would be categorized under so I have gone to advanced math since I have not learned how to do this myself. Anyways enough with an introduction onto the math. For my math I am going to use examples since I am looking for a formula not the answer to a single math problem. I think I was told once to look at multinomial theorem for this, but I'm not sure that entirely fits since I've never used it before.

Say I have five apples in a container. One of these apples is yellow and the other four are red. Every time I pull out an apple from this container if it is not yellow I put it back and therefore resets the possibility.

For this example let's just say I had the five apples in the container and I tried to get the yellow one in five attempts.
So basically there is a 20% probability to get it the first try and each try afterwards.

So effectively it is an array of 55 (3125) for combinations there are to this particular instance. What I still need to do is figure out a simple way to remove or combine all combinations that continue after obtaining the apple.

Example of something that needs to be removed or have it's chance of happening added to another instance: 1st attempt: Red, 2nd attempt:yellow, 3rd attempt:red, 4th attempt:red, 5th attempt:red

Which to my knowledge there isn't one(not really hard since I'm not as smart as a lot of people).

I understand the breakdown of smaller options like an array of 23​ would be easier to work with, but for smaller arrays like that my simple brain could break it down without a formula.

Edit: I just wanted to mention again I'm not actually looking for the answer to the apples example. I'm looking for the formula that would find the answer to that question. This is mind doing my simple math in my head without a formula I came to 38.25% on the apples example, but I was asking about a formula so I could do this for higher arrays like 3520​ and so forth.

Edit again: Redid what I did, came out with 66.72% probability for the apple scenario.
 
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I have no idea what this would be categorized under so I have gone to advanced math
Probability questions are usually best placed into the "Probability / Statistics" category. Thank you! ;)
 
Probability questions are usually best placed into the "Probability / Statistics" category. Thank you! ;)

Oh haha, I apologize I've been up all night now and I guess I passed over that before going into advanced(Makes me look pretty stupid haha). The thread seems moved now thanks.
 
I am currently looking for a formula and after an hour and a half of searching the web decided to just ask a math forum. I have no idea what this would be categorized under so I have gone to advanced math since I have not learned how to do this myself. Anyways enough with an introduction onto the math. For my math I am going to use examples since I am looking for a formula not the answer to a single math problem. I think I was told once to look at multinomial theorem for this, but I'm not sure that entirely fits since I've never used it before.

Say I have five apples in a container. One of these apples is yellow and the other four are red. Every time I pull out an apple from this container if it is not yellow I put it back and therefore resets the possibility.

For this example let's just say I had the five apples in the container and I tried to get the yellow one in five attempts.
So basically there is a 20% probability to get it the first try and each try afterwards.

So effectively it is an array of 55 (3125) for combinations there are to this particular instance. What I still need to do is figure out a simple way to remove or combine all combinations that continue after obtaining the apple.

Example of something that needs to be removed or have it's chance of happening added to another instance: 1st attempt: Red, 2nd attempt:yellow, 3rd attempt:red, 4th attempt:red, 5th attempt:red

Which to my knowledge there isn't one(not really hard since I'm not as smart as a lot of people).
Neither am I. If I were, I would be doing so much I wouldn't have time to be on this board!0

I understand the breakdown of smaller options like an array of 23​ would be easier to work with, but for smaller arrays like that my simple brain could break it down without a formula.

Edit: I just wanted to mention again I'm not actually looking for the answer to the apples example. I'm looking for the formula that would find the answer to that question.

You haven't said anywhere what question you are trying to answer. Is it "What is the probability that n tries are required to get a yellow apple"? Or is it "What is the expected number of tries before I get a yellow apple?"
 
You haven't said anywhere what question you are trying to answer. Is it "What is the probability that n tries are required to get a yellow apple"? Or is it "What is the expected number of tries before I get a yellow apple?"

The question I AM trying to answer is inside the wall of text I had, which was "What is the formula to find the answer to my example." apologizes if this seems rude, just trying to answer your question.
 
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