Probability of a getting a 5% result 2 times from 50 rolls

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NiaRya

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Apr 2, 2016
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An event having 5% chance to succeed. The event happening 50 times without affecting eachother. What are the chances of getting only 1 success in those 50 times? What are the chances of getting only 2? (My overall goal is determining the probability of getting less than 3 successes)

Im overwhelmed, I dont know what formulas to use for that. I dont know how to find out what formulas to use for that. I studied math and probability basics in school long ago but I didnt quite reach things at this level, Im also rusty and English is not my native language. I have googled probability tools a bit but was unable to find something aiding in this, though that could possibly be due to my lack of knowledge of the terms and mathematical language used for this kind of thing.

Ive determined (unless I messed up) that the average amount of successes should be exactly 2.5. I believe I can calculate the probability of getting 0 successes with (19^50) / (20^50) ≈ 7.7%. the median should be 2 I believe but that is more of an estimation based on observations from taking a similar simplified example with less rolls.

Any help or even a slightest nod in the right direction would be immensely appreciated =)
 
NiaRya said:
An event having 5% chance to succeed. The event happening 50 times without affecting eachother. What are the chances of getting only 1 success in those 50 times? What are the chances of getting only 2? (My overall goal is determining the probability of getting less than 3 successes)

Im overwhelmed, I dont know what formulas to use for that. I dont know how to find out what formulas to use for that. I studied math and probability basics in school long ago but I didnt quite reach things at this level, Im also rusty and English is not my native language. I have googled probability tools a bit but was unable to find something aiding in this, though that could possibly be due to my lack of knowledge of the terms and mathematical language used for this kind of thing.

Ive determined (unless I messed up) that the average amount of successes should be exactly 2.5. I believe I can calculate the probability of getting 0 successes with (19^50) / (20^50) ≈ 7.7%. the median should be 2 I believe but that is more of an estimation based on observations from taking a similar simplified example with less rolls.

Any help or even a slightest nod in the right direction would be immensely appreciated =)
Click to expand...

Looks like a binomial distribution to me. What do you think?
 
NiaRya said:
An event having 5% chance to succeed. The event happening 50 times without affecting eachother. What are the chances of getting only 1 success in those 50 times? What are the chances of getting only 2? (My overall goal is determining the probability of getting less than 3 successes)
Click to expand...

\(\displaystyle \dbinom{50}{N}(0.05)^N(0.95)^{50-N}\) is the probability of exactly \(\displaystyle N\) successes in fifty trials.
 
Thx yeah I never learned about that part of math :) Managed to have a friend explain the logic behind it too, didnt think it could be done that simply. Thx for replying!
 
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