Probability and chance of failure

AI Thread Summary
An experiment with a 96% success rate conducted 100 times has a 6.96% chance of experiencing exactly one failure. The probability of encountering at least one failure in those trials is significantly higher, at 98.3%. This calculation utilizes the Binomial Distribution to determine the probabilities for both scenarios. Understanding the distinction between "exactly one" and "at least one" failure is crucial for accurate probability assessment. Overall, the high likelihood of at least one failure highlights the importance of considering cumulative probabilities in repeated trials.
Zach_C
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Ok, not really homework but I did not want to crowd general math.

I have an experiment that has 96% chance of working. If I try it one hundred times what is the chance of one being a failure.

I know with a one in two shot it is .5^2=.25 You now have a 25 percent chance of failure. Any help. Sorry at the moment my brain seems dead.
 
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Oh my God I'm an idiot. I really am more tired than this thread let's on. :zzz:
 
Try solving the opposite problem.
 
Zach_C said:
Ok, not really homework but I did not want to crowd general math.

I have an experiment that has 96% chance of working. If I try it one hundred times what is the chance of one being a failure.

I know with a one in two shot it is .5^2=.25 You now have a 25 percent chance of failure. Any help. Sorry at the moment my brain seems dead.
Do you want the probability for "EXACTLY 1" Failure or for "AT LEAST 1" Failure?? Both can be determined from the Binomial Distribution:
Prob{Exactly 1 Failure} = (99)*{(0.96)^(99)}*{(1 - 0.96)^(1)} =
= (0.0696) = (6.96 %)
Prob{At Least 1 Failure} = 1 - Prob{Exactly 0 Failures} = 1 - (0.96)^100 =
= (0.983) = (98.3 %)


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