# Calculating Probability of Event After Y Attempts

• B
• Drakkith
In summary, the chance of event A occurring after Y number of attempts given X chance per attempt can be calculated by subtracting the probability of A not occurring from 1. If each attempt is independent and A has a probability of p to occur, then the probability of A not occurring in n attempts is (1-p)^n. Therefore, the probability of A occurring is 1-(1-p)^n. This includes all possible occurrences of A in the n attempts.
Drakkith
Mentor
TL;DR 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.

hutchphd
Wouldn't that be

0.15% = 0.0015

1000 x 0.0015 = 1.5 times

FactChecker
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 ##

Drakkith
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

hutchphd, jedishrfu and Drakkith
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.
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##.

hutchphd and Drakkith
Thanks all!

hutchphd
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.

hutchphd

## What is the formula for calculating the probability of an event after Y attempts?

The formula for calculating the probability of an event after Y attempts is P = 1 - (1-p)^Y, where P is the probability of the event occurring and p is the probability of the event not occurring on a single attempt.

## How do I determine the probability of an event occurring after a certain number of attempts?

To determine the probability of an event occurring after a certain number of attempts, you can use the formula P = 1 - (1-p)^Y, where Y is the number of attempts and p is the probability of the event not occurring on a single attempt.

## Can the probability of an event occurring after Y attempts be greater than 1?

No, the probability of an event occurring after Y attempts cannot be greater than 1. The maximum probability is 1, which represents a 100% chance of the event occurring.

## How does the number of attempts affect the probability of an event occurring?

The more attempts you make, the higher the probability of the event occurring. This is because each attempt increases the overall probability of the event occurring, as stated in the formula P = 1 - (1-p)^Y.

## What is the relationship between the probability of an event occurring and the number of attempts?

The relationship between the probability of an event occurring and the number of attempts is directly proportional. This means that as the number of attempts increases, the probability of the event occurring also increases.

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