Likelihood of things happening on with regularity depending on initial probability

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SUMMARY

The discussion centers on calculating probabilities using the binomial distribution, specifically for events with a probability of occurrence of 43.5% and 38%. The user seeks to determine the likelihood of these events happening a specific number of times over multiple trials, such as 12, 13, and 14 occurrences out of 15 trials, and 17, 18, and 19 occurrences out of 20 trials. The binomial distribution is identified as the appropriate statistical tool for these calculations, which involve fixed probabilities and multiple trials.

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ReamsOfVerse
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Hello All,

Firstly, what a wonderful place for people to help one and other. I am glad that I have stumbled across : )

I have posted this query in advanced because to me there it is advanced but if it is basic to others then please excuse me.

I can easily work out the probability of something happening every time at general probability or odds but I fall down when working out the probability of it happening a lesser number of times.

If there is a 43.5% of something happening on a single occasion.

If it is run on 15 occasions, what would be the chance of it happening 12,13 and 14 times.
If it is run on 20 occasions, what would be the chance of it happening 17,18 and 19 times.

If there is a 38% of something happening on a single occasion.

If it is run on 15 occasions, what would be the chance of it happening 12,13 and 14 times.
If it is run on 20 occasions, what would be the chance of it happening 17,18 and 19 times.

Any help, particularly in how I go about calculating so that I know for future reference would be a massive help.
 
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ReamsOfVerse said:
Hello All,

Firstly, what a wonderful place for people to help one and other. I am glad that I have stumbled across : )

I have posted this query in advanced because to me there it is advanced but if it is basic to others then please excuse me.

I can easily work out the probability of something happening every time at general probability or odds but I fall down when working out the probability of it happening a lesser number of times.

If there is a 43.5% of something happening on a single occasion.

If it is run on 15 occasions, what would be the chance of it happening 12,13 and 14 times.
If it is run on 20 occasions, what would be the chance of it happening 17,18 and 19 times.

If there is a 38% of something happening on a single occasion.

If it is run on 15 occasions, what would be the chance of it happening 12,13 and 14 times.
If it is run on 20 occasions, what would be the chance of it happening 17,18 and 19 times.

Any help, particularly in how I go about calculating so that I know for future reference would be a massive help.

Hi ReamsOfVerse,

Welcome to MHB! :)

This sounds like a problem using the binomial distribution. This is when an event can either occur or not occur with some fixed probability, and we want to run this experiment multiple times.

Have you worked with this before? Is this question for a course or just your own interest?
 

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