B Calculating Probability of Event After Y Attempts

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To calculate the probability of an event occurring after a number of attempts, one must first determine the probability of the event not occurring. For an event A with a 0.15% chance per attempt over 1000 attempts, the probability of A not occurring is calculated as (1 - 0.0015)^1000. The probability of A occurring at least once is then 1 minus this value, resulting in approximately 0.77712. This method highlights the importance of understanding independent trials in probability calculations. Overall, the discussion emphasizes the complement rule in determining the likelihood of an event occurring after multiple attempts.
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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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