Calculating Probability of Event After Y Attempts

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Discussion Overview

The discussion revolves around calculating the probability of an event occurring after a specified number of attempts, given a certain probability of occurrence per attempt. It includes theoretical considerations and mathematical reasoning related to probability theory.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant seeks to understand how to calculate the probability of an event occurring after multiple attempts, providing a specific example with a 0.15% chance over 1000 attempts.
  • Another participant converts the percentage chance into a decimal and calculates the expected number of occurrences based on the number of attempts.
  • A different participant presents a formula for calculating the probability of the event occurring at least once, assuming independence of attempts, and provides a numerical result.
  • One participant reiterates the expected number of occurrences and confirms the probability of at least one occurrence using the previously mentioned formula.
  • A summary post outlines the approach of calculating the probability that the event does not occur and then finding the complement to determine the probability of occurrence.
  • Another participant notes that calculating the probability of the event occurring directly can be more complex due to the various possible occurrences (once, twice, etc.).

Areas of Agreement / Disagreement

Participants generally agree on the method of calculating the probability of at least one occurrence using the complement rule, but there are varying levels of understanding and some participants express uncertainty about the complexity of direct calculations.

Contextual Notes

Some assumptions include the independence of attempts and the specific probability value provided. The discussion does not resolve the complexities involved in calculating the probability of multiple occurrences directly.

Drakkith
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TL;DR
Overall chance that A will occur given X chance per attempt and Y number of attempts.
Hey all. I've got next to no education in probability and I was wondering how to figure out the chance of some event occurring after Y number of attempts given X chance of happening per attempt.
For example, if event A has a 0.15% chance of occurring each attempt, and you make, say, 1000 attempts, what is the chance that A will occur?
Hope that makes sense.
Thanks in advance.
 
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Wouldn't that be

0.15% = 0.0015

1000 x 0.0015 = 1.5 times
 
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Assume that all the attempts are independent. The probability of ##A## occurring at least once would be ##1-ProbabilityThatANeverOccursIn1000 = 1-(1-0.0015)^{1000} = 0.77712 ##
 
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jedishrfu said:
Wouldn't that be

0.15% = 0.0015

1000 x 0.0015 = 1.5 times
Yes, that would be the expected number of occurrences of ##A##, assuming that all the attempts are independent. The probability of at least one occurrence of ##A## is 0.77712
 
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Drakkith said:
Summary: Overall chance that A will occur given X chance per attempt and Y number of attempts.

Hey all. I've got next to no education in probability and I was wondering how to figure out the chance of some event occurring after Y number of attempts given X chance of happening per attempt.
For example, if event A has a 0.15% chance of occurring each attempt, and you make, say, 1000 attempts, what is the chance that A will occur?
Hope that makes sense.
Thanks in advance.
The best approach is to calculate the probability that A will not occur. If each trial is independent and ##p## is the probability that A occurs in anyone trial, then the probability that A does not occur in ##n## trials is ##(1-p)^n##.

The probability that A will occur is then the complement of this, I.e ##1-(1-p)^n##.
 
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Thanks all!
 
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Note that the probability that A does occur includes all the cases where A occurs once, twice, three times up to all ##n## times. For that reason it's usually harder to calculate directly.
 
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