What are Bernoulli Trials? | Probability Theory, Bernoulli Distribution

What are Bernoulli trials? We go over this concept in today's math lesson, with several examples!

A Bernoulli trial is a random experiment with only two possible outcomes. One is usually considered a success, and has probability p, the other is considered failure and has probability q. Since one of the two (success or failure) must occur, we know that p + q = 1. Thus, p = q - 1 and q = p - 1.

An example of a Bernoulli trial is rolling a six-sided die, and consider success to be a roll greater than 4, and failure to be a roll less than or equal to 4. Then there are two ways for a success to occur (rolling 5 or 6), and 4 ways for a failure to occur (rolling a 1, 2, 3, or 4). Since all 6 numbers are equally likely to be rolled, we have that p = 2/6 and q = 4/6. Important to note is that there are six ways a dice can roll, but we can make it a Bernoulli trial by partitioning those possible outcomes into two disjoint sets, so that every possible outcome of the dice is either a success or a failure in our Bernoulli trial.

I hope you find this video helpful, and be sure to ask any questions down in the comments!

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The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.

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I like how you said in the beginning that it’s neat and not too difficult. Kind of helps with motivation since I’m searching about it on YouTube because it was hard to wrap my head around with this book I’m using. Thank you!

[ibejoseph]

This is beautiful. The best explanation I've seen so far on YouTube.👍🏽

[teosurch]

So simple and clear explanation, thank you!

[imposter]

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[northernswedenstories]

finally, someone who makes me understand it

[nandinimaurya]

Love from India Sir . Nice explaination ❤

[BEWAFASTATUSK]

Very good sir.. But please make some more video with actual problems solving of Bernoulli trials.

[careerstudy]

Thanks for the video and very helpful to understand the concept with example. Do we have more video on Probability distribution like Poisson, Normal, Multivariate Random Variables. Thanks Again!!

[KiranAshraf-pfzt]

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[jingyiwang]

Thank you so much for this amazing explanation! It is really helpful! Would it be possible if you could make a video series explaining everything about time series? Thank you so much in advance!

[jesusbermudez]

Yes, it has helped to understand Bernoulli trials. Thank you. Excellent video.

[Dan-ijei]

explained this way better than my professor

[omkargavhane]

nCr *p^r *q^n-r NOT EXPLAINED BINOMIAL DISTRUBUTION

[Noliyga]

I love ur videos it’s so helpful ❤ but I hope u adding translation in Arabic to make everyone understand

[putin_navsegda]

Good playlist, but it's SOOO introductory. No videos about multidimensional random vectors, math expectation., variance,
covariance, correlation, density, calculation for discrete and continuous random variables, Chebyshev's inequality, the law of large numbers...