# Binomial distributions | Probabilities of probabilities, part 1

Binomial distributions | Probabilities of probabilities, part 1

Part 2: https://youtu.be/ZA4JkHKZM50

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John Cook post: https://www.johndcook.com/blog/2011/09/27/bayesian-amazon/

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Dude you gotta release the other parts soon, I got an exam in statistics coming up😂👌

That means sucess rate can be find if we take more no. Of cases?

This video kept teaching me things I had forgotten from statistics right before I could remember them

I simply love all your videos, thank you!

This is a great example of the limitations of math models. The calculations are interesting and flawless, yet the model is clueless about how the world works (i.e. fake reviews) and thus useless in practice.

Can someone suggest a good, possibly almost complete book on probability theory for beginners?

The other thing is it is easier for companies to write a solid but small amount of face positive reviews but it much more effort and less likely for them to that in a greater fashion.

some added skepticism for me with the seller’s with fewer ratings is the likelihood that those reviews are bots or biased in some way.

Could you provide a way to determine between item reviews which aren’t only 0/1 reviews and for example are 0 to 5 Stars? Thanks as always.

Imagine having 5 arrows and probability of shooting 1 is 5/7

what is the probability that you hit exactly 5 times?

(5/7)^5

5/7 • 5/7 • 5/7 • 5/7 • 5/7

what if you have 6 arrows and want 5 of them to hit the target?

Well. It’s 5 for successes and 1 failiure

(5/7)^5 (2/7)

Now was is the probability that it will hit on 1, 2, 3, 4, 5 or 6th arrow?

there are 6 possibilities, 1 can fail, 2,3,4,5 or 6 can fail

Out of 6 arrows we *choose* 1 arrow to be a fail

(1C6)(5/7)^5(2/7)^1

and now expand the question to probability that 4 of them hit.

2C6 are possibilities

(2C6)(5/7)^4(2/7)^2

and in general we have

(nCr)((p)^(r-n))(1-p)^n

nCr(p^r-n)(1-p)^n

What is the probability of being suggested a multi-part lesson that starts at the beginning and flows continuously to the last part? I’m finding that it is so low, that it somewhat spoils the content.

Heeey 3Blue1Brown,

I kept a question in my mind.

In a test in which every question has 5 possible answers and only one is correct. A normal multiple choice test. If 870 candidates answered A, 30 answered B, 20 answered C, 40 answered D and 40 answered E, can we infer that A is the correct answer?

I enjoy your videos, thank you, bye.

What about the probability of giving a review? People might be more likely to give a review if they had a negative experience. So your actual chance of having a good experience could be greater than what the data from the reviews would indicate. Or maybe it’s vice versa. Maybe you are more likely to give a review if you had a positive experience. Thus swinging the actual chance of a good experience lower than what the data would indicate. How would this be accounted for?

"someone with a true perfect success rate would never have those two negative reviews" — this is assuming that the negative reviews reflected a failure on the part of the provider, but people leave bad reviews all the time for reasons beyond the provider’s control.

Furthermore, there’s an effect with online reviews where bad experience self-select to review the product or service more frequently than average experiences and extreme positive reviews tend to self-select more than average, but less than negative experiences. This generally gets into the problem of poor sampling and manipulation of the metric. Unless the review is mandatory the bimodal 1 and 5 star review distribution seems to reign. Then there are methods that are used by app developers to prompt first to see if the user had a positive experience, if so, ask them to review it, and if not, ask them to provide feedback (but crucially not link them to the reviews)

what about the probability of the unreported experiences? That is the probability that someone with a bad experience will bother to write a review, or that a problem with a vehicle will be caught on the line. or visa versa.

Can you please bring back the old title of:

"Which review sample should you chose Mathematically speaking?" .

We dont want to stumble on Mandela Effects.

Great vid.

Does NOT actually apply to Amazon!!!

From Amazon’s website:

//How does Amazon calculate star ratings?

Amazon calculates a product’s star ratings based on a machine learned model instead of a raw data average. The model takes into account factors including the age of a rating, whether the ratings are from verified purchasers, and factors that establish reviewer trustworthiness.//

You can also rule out negative reviews by reading them. Finding out if they are worth counting or not.

I flip a coin and it comes heads! I have the evidence the coin will give heads 100% of the time!!!🤣🤣🤣

I just want the part 2 and 3 now

In my model of what’s happening, I tend to assume that there are a few extra reviews from friends, employees, or alternate/fake accounts that bolster the positivity of the experience. Especially if there aren’t a lot reviews.

What id instead of just positive or negative reviews, ratings were on a 0 to 1 scale, 0 being completely negative and 1 being completely positive

Still waiting for part 2 hahaha

10:52 What’s the answear to the question I don’t get it why do the curves have different sizes. Is the area under the curve = 1.

how do you calculate that constat..like give me a general formula

How do you factor in the regular practice of sellers giving away free products for inflated reviews?

I just want to thank you for the series, that’s exactly what I need to understand for my upcoming maths finals, at least part 1 and two afaik

When’s part 2 coming out??

Well, while the video is a hundred percent correct from the math precpective, Amazon reviews are a little bit more complicated that a raw average of reviews ratings. I know there is a whole team of ML engineers who work on the model that adjusts these numbers

"assuming reviews are independent"…ready to see where this goes

Whats this therom called

I feel like your statement at 10:05 about "would happen one in a 1000 times" contradicts the whole point of this video, of probability vs data

Very nice

YouTube recommendations are weird

my brain over, sorry, ypu keep going..

Breath better, take a break from coughing

https://youtu.be/V7d62lwJ55Y

You are making things more complex.

plz do complex no series. i want it too badly

한글자막 감사합니다.

It’s amazing how probability can be both intuitive and unintuitive at different times. Like, humans tend to be good at intuitively understanding bayesian probability, but bad at intuiting other types of probability. I guess I shouldn’t be surprised though, since people are good at intuitively understanding certain types of math (like counting, addition, subtraction…etc.), and are completely baffled by others.

I don’t think Kruger and Dunning took into account me seeing this video 🤯🤯🤯

Suggestion! I noticed your use of colours to link values, I imagine the colours you have used would not have the intended helpfulness for people with colour blindness, perhaps try using blue/orange or red/orange instead as most people with colour blindness can distinguish blue. Thank you for the fantastic video, looking forward to seeing the rest of the series!

I made it incredibly simple… 200 is 3x more reviews than 50, 96% is 3% more than 93%, therefore, to me, they are exactly the same. I know this isn’t accurate at all, I should be good at maths, but I’m really not.

Oh my goodness, these videos are so awesome. I am stunned. I have a degree in statistics and I love this.

I’m 100% that 99% watching are as smart as 98% of the population and 92% left about 65% into the video

6:30 Monte Carlo go brrrr

자막 감사합니당

Didn’t understand anything, but it was very interesting.

This video is about to help some people get jobs

A bit late but can anyone tell me how to see which is best if there are more then 2 possible ratings? Like those 1-5 star reviews. Do I have to take an extra review of each possible rating and then take the average to find the "best" one