Probability of an event occurring at least once over n trials

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In summary, the formula for calculating the probability of an event occurring at least once over n trials is 1 - (1-p)^n, where p is the probability of the event occurring in a single trial. This is different from the probability of the event occurring exactly once, which only considers the outcome of the event occurring once. The number of trials directly affects the probability of the event occurring at least once, as more trials means more opportunities for the event to occur. The probability of the event occurring at least once is also influenced by the probability of the event occurring in a single trial, as a higher probability in a single trial results in a higher probability over n trials. However, the probability of the event occurring at least once can never
  • #1
helpmeplzzz
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There is a 1 in 4 chance that on any given sexual encounter, Joe will contract an STD. If Joe has sex 4 times, what are the chances of him having an STD?
 
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  • #2
Hint: what is the probability of not contracting after 4 times?
 
  • #3
1-(.75*.75*.75*.75) = my answer?
 
  • #4
Looks good.
 
  • #5
So how would you do it for the probability of Joe contracting an STD twice out of those 4 occasions?

I think you would have to do a combination for this?
 
  • #6
As this is misplaced homework-type question, I am locking it. This thread was also posted in the Precalc section under Homework & Coursework.
 

1. What is the formula for calculating the probability of an event occurring at least once over n trials?

The formula for calculating the probability of an event occurring at least once over n trials is 1 - (1-p)^n, where p is the probability of the event occurring in a single trial.

2. How is the probability of an event occurring at least once over n trials different from the probability of the event occurring exactly once?

The probability of an event occurring at least once over n trials takes into account all possible outcomes where the event occurs once, twice, three times, and so on, up to n times. The probability of the event occurring exactly once only considers the outcome where the event occurs once and does not take into account any other possible outcomes.

3. How does the number of trials affect the probability of an event occurring at least once?

The number of trials has a direct impact on the probability of an event occurring at least once. As the number of trials increases, the probability of the event occurring at least once also increases. This is because with more trials, there are more opportunities for the event to occur.

4. Is the probability of an event occurring at least once affected by the probability of the event occurring in a single trial?

Yes, the probability of an event occurring at least once is affected by the probability of the event occurring in a single trial. The higher the probability of the event occurring in a single trial, the higher the probability of the event occurring at least once over n trials.

5. Can the probability of an event occurring at least once over n trials ever be greater than 1?

No, the probability of an event occurring at least once over n trials can never be greater than 1. This is because the maximum probability of an event occurring in a single trial is 1, and as the number of trials increases, the probability of the event occurring at least once approaches 1 but never exceeds it.

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