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Text Comments (101)
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Amanda Boyd (8 days ago)

Can you bring a calculator to the interview?

Pratik Tripathy (16 days ago)

Perfect, the 10% probability reasoning is a killer!!!

I S (18 days ago)

Although the structure of the problem is sound the solution is flawed. You are asked to find the number of people wearing red. If someone is wearing 1 piece of red or 5 pieces of red does not matter. It is still 1 person, so multiplying 2 pieces by 10% is completely wrong.

Gauri chaturvedi (3 months ago)

Hii,
I had a question that what was the role of Monday in the problem which You did not consider in solving the problem.
so the first thing that came to my mind was that Monday is a working day , and red is not the color that you generally wear at your workplace and the second thing was that shouldn't we divide it into males and females as it red is considered to be girl's color, and then further divide is working and non working population, Pleas do let me know if I am wrong with my approach.
Thank you

George Ghorayeb (1 month ago)

I agree with you, I got an answer closer to 2 million people with this approach

rajat tripathi (2 months ago)

red is a girl's color? Since when?
I thought that crown is for one and only Pink

Jesterday Jambi (3 months ago)

7:50 Apparently your own answer didn't ring any alarm bells in your brain lol, 12.2 million means more than half the people should wear red. Also your approach does not eliminate double counting. If someone wears two or more pieces of red clothing, you count them multiple times. The question doesn't ask how many pieces of clothing worn are red but how many people wear red.

rima rai (5 months ago)

dear Everyone,
I know everyone is desperate to apply their calculations correctly, let me tell you this, YOUR RESULT, or IN FACT, THE CALCULATED ESTIMATED RESULT, DOESN'T REALLY MATTER TO THE INTERVIEWER. It's the approach. They aren't trying to judge what probability skills you can flaunt, they're there to judge what sort of approach you have applied. Please Calm down, and try not to focus on the end result!
Thank you!

Akhil Dhiman (7 months ago)

I was asked a ques in my Interview.
How many footfalls you are expecting in a marathon organised in your city??
Can you please suggest the solution for it
THanks

Dinesh Nemane (1 month ago)

90000 i think

Bo-Han Huang (9 months ago)

I think there's a mistake the author make.
When you define "any piece is on a person is red is wearing red". Then, you don't times "# of pieces". Instead, you use 1-prob(not wearing red)^(total piece). Here's an example, your equation will be @home=5%* [1-(1-10%)^(2)]. The illogical part is the author counts 1 person wearing 10 red pieces as 10, which is equal to 10 people with each wearing 1 red piece.

XINMIN CHEN (9 months ago)

The intro music is too loud...

Peter Szatoba (11 months ago)

12.5 million out of 20 seems ver unrealistic considering how uncommon red is as a clothing colour

hung nguyen (1 year ago)

McKinsey Vietnam has a low standard in their recruiting. Tip number 3: definitely could be more than 122mil if the chances of wearing red was higher since you have the multiple of clothing pieces lol...

Sakib Bazaz (1 year ago)

How did you manage to come with the percentages like 10% wears Red & 5% sit at home, etc. That does not make any sense.

Guderian0617 (1 year ago)

I am afraid I cannot follow your logic at all. For those who are going out twice, you are saying they have 10 pieces of clothing, with a 10% probability of each being red. Therefore you expect each person to have 1 piece of red clothing on them, which is absurd! You have managed to calculate the pieces of clothing that is red in NYC on a typical Monday (if that), not how many people will wear red.

Ritika Mital (1 year ago)

Dear Kim, Thank you so much for these lovely videos. It has really helped me clear the prelim interview rounds with almost no other preparation other than your tutorials !Look forward to learning more from you! Regards.

Christos Papadimitriou (1 year ago)

nice video. I liked it :)

Akshay Kotha (1 year ago)

What is a good source to think through different questions to get a flair of guessing and estimating within order?

Melaniatrumphasstockholmsyndrome (1 year ago)

Population of NYC is 8.6MM btw...Population of NY state is around 20MM.

M M (6 months ago)

Damn, that's what I thought! Thanks for the clarification - thought I was losing my memory!

Mankaran (2 years ago)

Hi Kim, thanks for the video. small question- is it not required to state the rationale behind choosing the % of people ate home work etc ?

Utkarsh Raj Singh (2 years ago)

Hey Kim, I am trying to guess the market size for a fashion based social network in India. Where and how should I proceed for guesstimating the market size & opportunity ?
Thanks.

Ege Öncel (2 years ago)

Your calculation about red is wrong. Other than that, great video. Third group should be named those who went out twice but did not wear red at the first time.

Alessandro Takeshi Morita Gagliardi (2 years ago)

Your math here is a bit flawed. If a person wears, say, 5 pieces of clothing, the chance that at least one of them will be red is 1-(0.9^5), i.e. one minus the chance none of their clothes is red, which is about 41%. Similarly, if they wear 10 pieces of clothing, their chance will be 1-(0.9^10) which is about 65%.

Shaurya Rastogi (1 year ago)

Absolutely point on! Apart from that, there is one more thing which is wrong. When the guy is multiplying 1 million x 2 pieces x 10%, he is essentially finding the number of pieces which are red and not the number of people. One should understand that when one says 10% (again which is not correct, it should be 19% according to the correct way), we already mean that when 1 million people wear 2 pieces, 10% of those 2 pieces are red meaning 10% of the people are wearing red in some capacity. So, we just need to do 10% of 1 million to find the people. The correct calculation would be: 1 million x 19% for the first part.

赵曦蕾 (2 years ago)

The answer is flawed. If people who are going out twice wear 12 pieces instead of 10, we will have the probability of wearing red equal to 120%, which does not make any sense. Actually, the answer shouldn't be using 10*10%; instead, it should be 1-0.9^10 = 0.65.

Lê Duy Hoàng (2 years ago)

I agree, it should be 1-0.9^10 for more accurate number. Good catch!
But I think Kim just want to simplify the answer. His answer would totally make sense if you assume that people want to wear items with different colors and people also want to have different outfit from each other. 120% should be considered as 100%. people wear 11, 12 piece or more than 10 pieces in general will be counted as wear red. There is no set answer for a guesstimate so you can align with the interviewer to keep your calculation simple. Save your time & effort for other parts.
Well, it's more important to grasp the insights Kim shows later in the video. I found it much more meaningful than the example's solution. We will be unlikely to be asked the same question when come to our real interview. Learn the methodology to solve every question, then develop our own answer for each specific question given in real case.
Cheers,

ssanvit (2 years ago)

Thanks for taking out the time to make this video , but I am sorry to say that your calculations are completely wrong and this video needs to be taken down immediately , else you are going to misguide many people out here .I will just point out to one mistake and you can figure out the rest. for @home ppl you say they wear 2 pieces of dress and the chance of the colour is 10%. This means in order to calculate the total number of ppl possibly wearing red is 0.19*5 million. It is 0.19 because you need to calculate the probability of one of the suit pieces being red which has a 0.19 probability assuming only 10 colours are under use.

Alex Reinhart (2 years ago)

By that logic, if someone was wearing 10 pieces of clothing then they would have a 100% chance of wearing red. The 19% Ssanvit is referring to is the 20% you calculated (2 pieces x 10% chance of red) minus the chance that both pieces of clothing are red (to avoid double counting, so in this circumstance 10% x 10% = 1%. 20%- 1% = 19%).

Belisa A. P. (2 years ago)

If chance is 10% and you got 2 pieces, it should be 1-(1-10%)^2 which is not so much different for 2 pieces, but if you got 10 pieces, then it's way different. If you have 12 pieces, then you are more than for sure wearing red?? No.

John Doe (2 years ago)

Sorry bud but Belinda (and many others) are right. Not a big deal. Just goes to show you don't need to be a genius, or even literate in middle school math for that matter, to be a Mckinsey consultant. (Either that or you're not who you say you are.)
You seem genuinely confused so I'll make it simpler. If you go into your example and assume everyone in NY wears 12 pieces of clothing (a bad assumption but not technically impossible), you would conclude that more than 20 million people are wearing red. That's not possible.

Belisa A. P. (2 years ago)

If you have two pieces, each has 90% possibility to be NOT red, then the chance that NONE of them is red is 90%^2=81%, instead of 90% x 2 = 180%. As a result, the odds that you have at least one red piece is 1 minus the chance you get something red: 1-90%^2.
If you have any questions, please consult any probability textbook around. Probability cannot be more than 1 by definition. I like your videos and hope you consider this seriously.

Parantap Singh (2 years ago)

Hey, nice video. I had a doubt. The question mentioned the number of people wearing red and not the number of red clothing articles that they are wearing. So, should we have multiplied the average number of clothes a person wears to get the final answer ?

Rodrigo Aoyagi (2 years ago)

Shouldn’t we consider the number of tourists visiting the NY Metropolitan area on a typical Monday in addition to the population?

Aditya Kondejkar (2 years ago)

1st of all video has cleared all my doubts
having one problem
I can't find link for e book of case studies .
will you share it again?

M M (6 months ago)

Thank you!

MAYANK PRATAP SINGH (2 years ago)

Read "Case in Point". It will help.

Isis Tian (2 years ago)

New York City's population is 8.4m, NY State is about 20m. Just for your information...I like the way you do it tho. :)
http://population2016.com/population-of-new-york-in-2016.html

Chirag Tibrewal (2 years ago)

There are sometimes supply side and demand side approaches being mentioned like McDonalds sale on a particular day can be calculated by the supply side or the demand side. Which one to follow when?

Sigbjörn Ekman (2 years ago)

NYC population is rather around 8.5 million while the state is about 20 million. Just for information. Doesn't affect the method you demonstrate :)

Lucy Liu (2 years ago)

Do you have a resource or list of numbers we should memorize for estimation type questions (ie. population of the 5 largest countries in the world, population of NYC and LA, volume of a boeing 747, length/width/depth of a standard sedan, height of average skyscraper, etc.)?

Sahil Shah (2 years ago)

I believe you can assume some of these things. Again, its your approach that is important and being tested. No one cares if you know the length of a sedan. As a consultant, flexibility is key. You'll have the data either given to you, or you can GUESSTIMATE.

Prasanth Padmanabhan (2 years ago)

(you spelled hassle wrong - it shows hustle in the video btw)

Prasanth Padmanabhan (2 years ago)

WOW! SUPER AWESOME! And SIMPLE to FOLLOW!!!! You're my hero.

DoCoMo661 (2 years ago)

I thought the interviewer said "do not count them twice", so that means in the scenario with people going out twice a day, and each time wearing 5 pieces of clothing, we should simply count it as 5 pieces of clothing and not 10 pieces right?

Sanmaya Jolly (1 year ago)

To be counted in the result as "wearing red", you only need to have one piece of clothing red any time during the day for as little or as long. People going out twice implies that they have changed clothing. Going to work in the morning and maybe out with friends or running errands in the evening. If you're going out a second time, for a different reason, it usually has you dressing differently. That is why "work" only people were counted separately.
Now, given that they're changing clothes, it makes them wear 10 pieces a day. Color percentages are kept at the standard 10% for keeping the math simple.
Well this is how I feel it should be solved. But it's only guessing and estimation, so feel free to suit it to your own style.
Cheers

Vidyasagar Battula (2 years ago)

Even I felt the same.

Arthur Lyra (2 years ago)

Let's say the chances of a piece being red is 20%, not 10%...
Your answer would be 24.400 million people!
How's that math ok?
Even if the chances were 100%, your answer could not go over 20 million

Eberneezer Loose (2 years ago)

I agree with you. Had I been the evaluator I would not have passed the candidate.

Arthur Lyra (2 years ago)

+lfr0nald0 Yeah, I agree with you that it's necessary to think outside the box to draw different conclusions, but you have to agree with me that the question he had to "answer" was "How many people wear red in New York on a typical Monday?", however he ended up answering "How many red pieces of clothing are worn in New York on a typical Monday?".
Can you see that? He was just one step short of answering the actual question, but he didn't.

lfr0nald0 (2 years ago)

+Arthur Lyra other conclusion is that people are wearing more than one piece of red clothing. In this calculation he did not assume that people had to wear only one piece of clothing. I think more than the final number, you have to think outside of the box to draw different conclusions

Hooman Moayyed (2 years ago)

If I were the interviewer I would have failed you immediately for lacking a proper sanity check. According to your example, the chances of someone wearing red on a particular Monday would be 60%. Out of 10 colors and a 10% chance, The number should be no higher than 2 million.

Simone Buckinger (2 years ago)

Woah, this video is awful! Why does it get so many upvotes?!
1) Completely wrong calculation!!! Chance of wearing red = 1 - chance of not wearing red = 1 - (9/10)^n pieces...
2) No specific preference? Really? I don't think that i've got a single red pair of clothing... most socks are black, undies black or white or blue or green but not red, jacket not red etc...
The whole calculation is retarded... With a simple "hm population is 20M and about every 5th guy/girl wears red so about 4M wear red" you'd be way closer. and about the clarification... what does it mean for a piece of clothing to be red? If I have a half red, half blue shirt is it red then?! Is my ketchup stain enough? Or does it mean completely red from A-Z?!

Smriti Mahendru (2 years ago)

Hi, In case I don't have any idea about my market size, what should be a approach ? For example you knew about 20 million population which is near true 23 million. For example if someone asks me "Estimate the quantity of wine consumed in Delhi in one year?, what will be an approach and answer ?

Zeeshan Saini (9 months ago)

Maths was never the focus, the apporoach was.

shivangi nassa (2 years ago)

What does going out twice here mean?

ConquerIITJEE (2 years ago)

What does going out have anything to do about it??

Nithin Karnati (2 years ago)

Going out wear 5/10 pieces as opposed to staying home wearing 2 pieces. So chances of finding red are high among people going out

Rajendra Singh (2 years ago)

very helpful . thankyou so much

Albert Hall (3 years ago)

Thank you a lot from Russia. Very nice approach which I add to my arsenal,),

Akshay J (3 years ago)

figures like NY population being 20mn are tricky....we need to know realistic assumptions here....any pointers? Why 20 mn?

Akshay J (2 years ago)

+MConsulting Prep Alright, Many Thanks.

hemant dhaked (3 years ago)

very helpful

Akash Deep Choudhury (3 years ago)

Correct me if I am wrong. I think there is a flaw in your answer. You multiplied %of people*no. of pieces*chances of being red to get the 'no. of people', which is incorrect. Think of it this way - Had there been a total population of 100 people wearing 3 pieces having 100% chances of wearing one piece being red, the answer will yield a total of 300 people wearing red which is greater than the total population! Correct approach should be %of people*chances. The number of pieces should be factored in while calculating the chance of wearing one red.

Sree Charan Shatdarsanam (2 years ago)

+Akash Deep Choudhury yeah in your example of 100 people, yeah number of pieces as a factor is incorrect, makes sense, it should rather have been 100 people * % of red per dress [which has 3 pieces having 100 % red which is 3*100% = 3 (being > 1) ==> 100% of dress having red]
if 'x' pieces have 60% chance of being red and that turns out to be > 1 it should be considered as 100% of being red in your dress, that was a flaw in the explanation
But having this, the approach was good ,
NYC Population
% distribution based on a factor of indoor vs outdoor (more than once included)
% of having red in your dress

Md Shams (3 years ago)

simple and easy to understand.. Thank you

黄晖凯 (3 years ago)

Thank you from China:) !!!

Rafael Machado (3 years ago)

I bought 2 help packages from this website: CONSULTING MATH and Case Interview End To End Secrets.
THE PROBLEM IS: I`ve lost my PC and the files in it.
Now that im traying to contact them (coz the download links expired) I have no feedback from them.
Long history short: You will pay a lot for a desastrous costumer service.

Ahsen Parwez (3 years ago)

Hi! In the last sector "going out twice" which constitutes 5 million people (or 25% of NY population), the number of people wearing red comes out to be 5 million. Doesn't it seem counter-intuitive? We took a group of 5 million people and our calculation shows that all of them are wearing red.

Nathan Walters (3 years ago)

+Ahsen Parwez I think the way to think about this it is like this. Of those people that go out twice on a Monday in New York in two completely different outfits (10 items), there is a very high chance 1 item will be red. Now this is based on fairly unrealistic %s in a very basic model - but the point of the video is to show a methodology within a time constraint so the actual answer is less important than having a structure in place before calculating it

Shadow (3 years ago)

+Ahsen Parwez Guess his "alarm bells" and consistency checks were turned off...

Jasleen Kaur (3 years ago)

While solving guesstimates in front of the interviewer, do we talk loudly even while thinking about the answer?

Ko Yoonji (3 years ago)

Hi, thanks for the excellent video that explains things clearly! I had one question though. I learned that all factors need a logical explanation, but you seem to just make an assumption that 5% of the people stay at home, 75% of the people go out once and 25% of the people go out twice without much explanation. Is a logical explanation unnecessary for this assumption? If so, to what extent do we have to give logical explanation, and to what extent can we just make free guesses?

David Budden (3 years ago)

Thank you for the excellent video! My only criticism is that your analysis presumes that, if there's a 10% chance of wearing red and you wear 10 items of clothing, there's a 100% chance of you wearing red. This is obviously a simplification, in the same sense that tossing two coins doesn't guarantee a 'tails', or that wearing 20 items of clothing doesn't give you a 200% chance (applying sanity checks as suggested)
The chance of "wearing red" with ten items is 100% minus the probability of none of the items being red, i.e. 1 - (1-0.1)^10 = 65% (using your assumptions)
If people are going to use this approach, I would suggest they explain to the interviewer that it's a rough estimation technique that makes the analysis simpler and is suitable for SMALL values of N (# items worn) only. In the case of 10 items, 65% is very different from 100%. For a smaller value (say, n=3), 27% (correct) is not so different from 30% (incorrect)

Ankita Mehta (3 years ago)

+David Budden Hi, I think I view this slightly differently. Your calculation assumes AND not OR. Any one piece or more than one piece of clothing could be red. The probability of this is 0.1+0.1+...10 times. 0.1*0.1*0.1... will give you the probability of wearing all pieces of red colour. (1-0.1) is the probability of not wearing a red shirt. (1-0.1) is the probability of not wearing a red pant. Multiplying these two make the two activities dependent. However, these activities are independent (i.e, wearing a red shirt does not determine whether you will wear a red pant or not)

Chaman Chutiya (3 years ago)

Appearing for Bain this weekend. Nervous as hell.

M M (6 months ago)

So what happened??

Aakash Mehta (3 years ago)

don't count them twice, but you counted people wearing red twice at 25%? is this because you assumed people changing into different clothes (different article of red) should be counted twice? I think that number should be halved or this needs clarification as to if different clothes but same person counts as two

Quanita Ahmed (4 years ago)

Hi,
If we're told to not count people going out twice, why do we include them in our analysis?

Nicole Bills (4 years ago)

Where did you get your population figures from? They seemed off to me, and according to The Google, NYC's population is 8 million. There are only 19 million people living in New York state.

Julie B. Davis (2 years ago)

No, it's not. NJ has a very large population that isn't located anywhere near NYC. The more accurate way to factor this in is to make an assumption about the commuter population fron NJ, CT and Long Island (which isn't a part of NYC proper and doesn't get counted in statistics, despite having a high commuter population. It's less that the (completely off base) 20 million number matters, more that how you arrived at that number is impractical

Ahmed Elkomy (4 years ago)

Great session, I really enjoyed it. Thanks

kcazaa (4 years ago)

In this example, would wearing red underwear count as wearing red? If that's the case the first group of people might be higher.

Anuj Kathwariya (4 years ago)

Its really helpful. Thank You.

Betsy (4 years ago)

thanks for the simple and structural instructions

fedarduino (4 years ago)

Hi, sorry to write you, but I believe that your reasoning is wrong.
If, for example, you have 2 pieces of clothing and the chances of wearing red are 10%, the probability of having something red is equal to P={1 - probability of not having something red}, i.e. 1-(9/10)^2=0.19.
Similarly, if you have 5 pieces it will be 1-(9/10)^5=0.41 and if you have 10 pieces it will be 1-(9/10)^10=0.65.
This will lead to very different results with a total of 9.18 million instead of your 12.2 million.
If you need clarifications let me know. What you are basically saying here with a simpler case is that if I toss a coin 2 times the probability of having at least one head will be 100% (2*50%) that is quite wrong.
Please edit the video!!

shashank dave (3 months ago)

+Steven Yu yeah.. instead of "one piece red" it should be "atleast one red"

Lucas Bianchi (10 months ago)

Completely agree! Though I was doing something wrong, but the calculation is wrong. What they are calculating is the amount of red pieces of clothing, but they are not considering that a person might have 2 or 3 or more pieces of clothing red.
Just a quick way to understand that this is wrong. We can review the logic behind the people how go out 2 times. What they are saying in this video is that all of them (100% (10x10%)) will were something red on Mondays. NOT correct.
Thanks for leaving this comment. Helps to get it right.

Gonzalo Izaguirre de Diego (1 year ago)

Ankita Mehta Ankita Mehta Ankita Mehta Well, so following your reasoning if someone wears 11 pieces, the probability of wearing one red si 11*0,1 = 1,1. Thats nonsense.
If you pick n pieces of clothing randomly, simplifying (we asume after choosing one red the probability of choosing later red again is the same), the probability of choosing at least one red is 1- choosing no red pieces. Choosing no red pieces' probability is 0.9^n (when two events are independent, probabilities are multiplied, no added; for example, probability of having two faces when you throw a coin is 0.5*0.5 not 1). So the probability of wearing AT LEAST one red piece is 1- (0.9)^n.

Ankita Mehta (3 years ago)

+fedarduino Hi fedarduino, I understand where you're coming from but I think the underlying assumption you've made is incorrect. I think the assumption that was made in the video was the probability of "wearing something red" not "having something red". The key assumption here for simplicity is that people would generally own an equal number of pieces of clothing of 10 different colours (i.e 5 white shirts/pants, 5 red shirts/pants, 5 black shirts/pants etc). Therefore, the probability of picking a red shirt is 5 out of 50, which is 10%. You're assumption of "having red" means that people generally own one colour of clothing (i.e one of 10 colours).
The two events- wearing a red shirt or wearing a red pant (or both) are independent events and therefore need to be added (i.e 0.1+0.1), not multiplied as (0.1*0.1) will give you the probability of wearing a red shirt and a red pant, which is wrong.

fedarduino (3 years ago)

+Steven Yu Hi, I believe this is the easiest way to calculate the probability but there could be other ones as well (as a tree diagram for example). In probability when P=1 it means the probability is 100%. In this case, if you want to compute the probability of having something red the easiest way is to compute the probability of not having something red and subtract it from 1. To get this, you just need to multiply your chance of not having something red by itself as many times as the pieces that you have. If you have 3 pieces it will be 9/10*9/10*9/10=(9/10)^3. It's hard to write you the theory behind in a Youtube post, but if you just google 'probability' I am sure you will find a lot more info related to this.

Ngoc Vinh Nguyen (4 years ago)

Hi Kim, is this you, who was talking in the video?

Kim Tran (4 years ago)

Hi Adrian,
Thanks for the great question! The short answer is No! You may ask the interviewer these types of input data.
Here 's the long answer. So the key to Market-sizing or Guesstimate questions is your methodology of breaking down the big and vague goal into smaller bite-size pieces. So as long as you do that, it's completely ok to ask for data on those bite-size pieces.
As a bonus, I will give out a tip you should take when asking for that bite-size pieces (in this case is the NY population). Don't just ask for the data, also tell the interviewer how you (in normal situations) would do to find out about that data. In this particular case, I would say something like:
"Now that I have broken down the problem into smaller pieces, I would like to get input data on one of those pieces, the NY population. In real-life situation, I would Google to get it!"
Hope this helps! Good luck!

Adrian Obleton (4 years ago)

Thanks. If I were really trying to estimate these numbers I would use google to get an estimate of the needed demographic information, so it makes sense that in an interview I would be able to ask for that information.

Adrian Obleton (4 years ago)

What would you do in a situation like this if you don't know the popukation of New York? My estimate of the population was way off. Should we just memorize some basic demographic information?

ominous450 (2 years ago)

It could help but I wouldn't recommend it. The market-sizing & guesstimate question can be about anything. For example, how many gold balls fit in an airplane??? They don't expect you to memorize the volume an circumference of those things.

tuan hai Chu (4 years ago)

Cool video

Saigon League (4 years ago)

Wao!! Thanks a lot!

charan teja (4 years ago)

ThanQ

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