MHB Likelihood of things happening on with regularity depending on initial probability

AI Thread Summary
The discussion focuses on calculating the probability of events occurring a specific number of times based on given probabilities. The original poster seeks guidance on determining the likelihood of an event with a 43.5% chance happening 12 to 14 times over 15 trials, and 17 to 19 times over 20 trials, as well as similar calculations for a 38% probability. A response indicates that this scenario can be addressed using the binomial distribution, which is suitable for experiments with two possible outcomes. The poster is encouraged to clarify their familiarity with this concept and the purpose of their inquiry. Understanding these calculations can enhance future probability assessments.
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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