## Recommended Posts

This is a pretty interesting paper:

and here are the test questions:

(1) A bat and a ball cost \$1.10 in total. The bat costs \$1.00 more than the ball. How much does the ball cost? _____ cents

(2) If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets? _____ minutes

(3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake? _____ days

Here are some interesting stats from this test:

http://img9.imageshack.us/img9/9774/crtt.jpg

Pretty amazing that the 25% of the population of Boston sitting around waiting for the fireworks show got all 3 questions right.  The last question, without the aid of a calculator, requires a little bit more sophisticated mathematics than what I would expect the average Joe to know to answer it.  Not surprising, almost half of those at MIT who answered the 3 questions got all 3 right.

##### Share on other sites

I won't start answering because I thought that it was fairly easy except when I read the paper the answer for the third question was not the one I imagined.  After further thought,  I think the paper is wrong.  I actually hope that I am wrong and not the paper because that would mean that a whole bunch of people either didn't check their work or the entire study is worthless!

##### Share on other sites

Hey pof, actually, the answer in the paper is the correct one.  Ping me via PM if you want to discuss.

##### Share on other sites

All three questions are very easy. I guess most people will answer it correctly if they have taken some analytical exam. What I meant was that if you have taken exams such as Quant potion of GRE then you can answer these kind of questions easily and quickly because basic questions there are similar in nature and you become tuned to think certain way. Though I took it many years ago so format might be different nowdays but 3 questions mentioned here were not difficult to start with.

##### Share on other sites

"Quant potion of GRE " ---- Correction , it was Analytical section not the quatitative section.

##### Share on other sites

I love these kind of quiz!  :) Please keep posting some from time to time!

In elementary school, the best course memories that I have was when the teacher was putting 2 lines of student and was asking simple math questions (like 9+6, 17-9, etc.). The first to give the good answer was winning, and the other one was out. The goal was to have all the people in the other line out!

They used to put me last on line to save our team in the ultimate case  ;D

##### Share on other sites

Here's another famous question (if you know the answer don't say it):

A gameshow host invites you to pick one of three doors. One door leads to a brand new Rolls Royce. The others lead to goats. After you make your choice, the host will make the game easier by opening one of the doors hiding a goat.

Do you now stick with your first choice, or do you pick the second door?

##### Share on other sites

you pick the 2nd door

##### Share on other sites

Here's another famous question (if you know the answer don't say it):

A gameshow host invites you to pick one of three doors. One door leads to a brand new Rolls Royce. The others lead to goats. After you make your choice, the host will make the game easier by opening one of the doors hiding a goat.

Do you now stick with your first choice, or do you pick the second door?

I don't know the answer but here is the my take on this.

I see 3 possibilities( meant I can pick either of three spots),

1) If my 1st choice happens to be car then if I switch then I am stuck with getting the goat

2) If my 1st choice happens to be first goat then by switching after seeing the 2nd goat in another spot, I will get the car

3) If my 1st choice happens to be second goat then by switching after seeing the 1st goat in another spot, I will get the car.

2 out 3 times I will get the car by switching so 66.66% chance of me getting the car by switching.

So, If I want the car then I will switch but if i want the goat then I will not switch my choice:)

kawikaho - My last name is Ranjan and first name is Rohit so you might be referring to some one else.

##### Share on other sites

Good thinking Rranjan. I like that problem because it demonstrates the difference between intuited odds and logical odds. If you wikipedia Marilyn Vos Savant, the problem apparently provoked strong reactions amongst even trained mathematicians.

##### Share on other sites

Not surprising, almost half of those at MIT who answered the 3 questions got all 3 right.

I was very surprised. I'd expect much better results, from any institute of technology.

##### Share on other sites

On the first round, obviously, my odds to get the car are 1/3.

Then, unless he open the door of my first choice AND one of the two doors that has goats in it, on the second round, my odds to get the car are 1/2. If he opens the door of my first choice and another door that has goats, it would be stupid because my odds that I would find the car door would be 100% next round.

Let's say that I've choosen the first door and, then the host open the second door (goat). Anyway, if I keep the first one or switch to the third one, the odds are 1/2 now anyway.

Le'ts say that I've choosen the second door and then the host open it and I see that it has a goat in it. It would be foolish to keep my first choice because I would be 100% certain that it would have a goat in it.

##### Share on other sites

Partner24, the key to the puzzle is that the presenter always follows your guess by opening a door with a goat. If he opened a door at random, and it happened to be a door with a goat, then you have a 50-50 chance of selecting the car, and therefore receive no benefit from switching your answer.

Also, I should have made this clearer, the host will always pick a door different from your first pick. Otherwise, there would be no point in asking whether to stay or switch.

##### Share on other sites

Thanks for the Rabbitisrich, that's an interesting quiz.

The fact is the host increase my odds from 1/3 to 1/2 after the opening of the door with a goat. There is then no value added by switching my choice from one to another. Either way, I'll still have 50% odds.

##### Share on other sites

Partner, there is a beneft to switching.  You can try it and see what the results are.  However, an intuitive "proof" that might help is if you take the same problem to 100 doors.

Suppose instead there's 100 doors, 1 car and 99 goats.  Suppose you choose door 1.  Then the host opens doors 2, 3, 4 ... 56, 58, 59, ... 100.  So there's exactly 2 doors closed, door 1, which you picked, and door 57, which the host decided not to open for some strange reason.  Would you still claim that there's no benefit of switching from door 1 to door 57, that it's still 50/50?

I think it's the same question, just reframed.

Richard

##### Share on other sites

Ahaha you had me on this one!  ;D

Cheers!

##### Share on other sites

Not surprising, almost half of those at MIT who answered the 3 questions got all 3 right.

I was very surprised. I'd expect much better results, from any institute of technology.

Very true, but MIT isn't all about engineering, sciences, and mathematics.  It does have other fields of studies.

##### Share on other sites

Partner, there is a beneft to switching.  You can try it and see what the results are.  However, an intuitive "proof" that might help is if you take the same problem to 100 doors.

Suppose instead there's 100 doors, 1 car and 99 goats.  Suppose you choose door 1.  Then the host opens doors 2, 3, 4 ... 56, 58, 59, ... 100.  So there's exactly 2 doors closed, door 1, which you picked, and door 57, which the host decided not to open for some strange reason.  Would you still claim that there's no benefit of switching from door 1 to door 57, that it's still 50/50?

I think it's the same question, just reframed.

Richard

That is an EXCELLENT way of reframing this problem to make it more obvious.

There are caveats to the Monty Hall problem that were already mentioned.  They are subtle, but very important.  And Marilyn Vos Savant is really a genius.  She was getting lambasted from many math Ph.D's, and ridiculed by others as well.  Although, it makes me wonder why someone would squander such talents as a columnist vs. helping the world become a better place to live in.

##### Share on other sites

the CRT was pretty easy.

I found the article on the blog quite interesting.  Thanks for the link.  They call this test a kind of a "cognitive illusion".  Don't make snap judgments on questions that seem really easy.

On the other hand the Monty Hall problem is a problem, and appears as such.  I was having a horrible time trying to explain it to my kids and guests over dinner the other day.  Nobody got it and my explanations almost convinced me that I was wrong to switch doors:-[  The 100 door example is a great intuitive aid.

##### Share on other sites

This is an interesting problem with practical applications. If you use the investment banks as a proxy for the doors then you would clearly improve your returns by selling one investment bank and purchasing another after the goat Lehman Bros or Bear Sterns is revealed. Also it is humorous to consider that as value managers we actively select invest in the doors that have had goats revealed frequently behind because we understand that the true odds of a goat being revealed on subsequent openings is dependent on the total number of goats in game. Unless of course there is some sort of contigent probablility at work.  In the real world it does seem that a door that has revealed a goat in the past does seem to have higher chance of revealing a goat in the future.

## Create an account

Register a new account