Thursday, August 30, 2007

Answer to the Hidden balls problem

Click here for the question

The answer is 1/3.

The technical way to go about the answer is thru conditional probability. But that is the laborious way and CAT is not forgiving on those who take time to solve the problems :)

The key basic idea to learn here is that when you dont know what balls were taken out, it does not change the probability. Hence the probability would remain the same 1/3 even if Ashok had removed 0, 1, 2 or 3 balls.

If this feels unintutive, just think that if Sunita had put here hand inside the bag and randomly put aside two balls without looking and then choosen the 1 ball from the rest, the ptobability would still have been the same. What Ashok has done is equivalent to this action

Now think about a small variations.
If the probability does not change when Ashok removes 0, 1, 2, 3.. balls, does it change if he removes all the balls. If so what is wrong in our thinking

Click here for the question

Tuesday, August 28, 2007

Problem 2 - The hidden balls

For the last problem 72 people visited the blog, but only 2 posted the answers. Dont be shy in putting the answers, you can even do it anonymously or with a pseudoname. Only then can you gain confidence

Here comes the second problem. And as i have said, it is simple yet you need to have your basics perfect to answer these.

"There are 3 black, 5 red and 4 green balls in a bag. Ashok comes in, takes two balls at random and walks away with them. Sunita comes and picks a ball from the bag. What is the probability that the ball Sunita picked is green"

Think carefully before answering.

Click here for the answer

Answer to the fake note problem

Click here for the question

Got a mail saying that some people at Pagalguy got it right. I dont mind people posting the questions on pagalguy, since it would benifit more people. But if you guys can also put the answers here, it would benifit all and also help me answer queries
Yes the answer is $5. Here are some fundas on how to think simple and not get confused.
1. Lenovo's loss has to be somebody's gain. Dell gained $5 (he started with a fake note ehich was equivalent to 0) and Acer gained/lost nothing.
2. If the note was not fake, no one would have lost anything. The note being fake is equivalent to Acer misplacing the $5.
3. The only thing that got destroyed is the $5 note and hence that is the loss.
Hope it clears things. This problem was just to demonstrate how we make silly mistakes in simple everyday problems. I am sure if you were Acer yourself (a small kirana shop owner), you would have realised your loss amount easier :)

Click here for the question

Monday, August 27, 2007

Problem 1 - Fake Note problem

Hey guys,

It has been a long time since I wrote on the blog. I had said that I would come up with a website to help people preparing for CAT after I got a good response for the GD and PI preparation. But, since I had to travel overseas on some assignment for three months I could not devote enough time to get the website on. So I thought that atleast I should devote some time for your CAT prep. So I will be putting some very very simple but interesting problems on the blog that people can come and answer. I promise enough traps in each problem that will help you hone your basics.

Most problems will be on probability, which people find hard to master and I think I am fairly good at. But let me start with a simple arithmetic problem. It will be on for a week and people can post their answers with reasons on the comment section.
Rope in as many guys as you know. More guys, more perspectives and better learning.

So here goes the first problem.

Dell goes to a store to buy a new cheap ipod that has come in the market. He gives $5 to Lenovo who is the shop owner.
The ipod is worth $3, but Lenovo does not have change. He goes to Acer who owns a “pc world” next door and gives him $5 to get back five $1 bills in return.
He comes back and returns $2 to Dell and gives him his ipod.
After a while Acer comes and says that the $5 bill that lenovo gave was a fake one. Lenovo is disappointed that he got cheated, but gives Acer a new $5 and tears the fake bill.
How much does Lenovo lose?

The choices are a) 5 b) 7 c) 10 d) 3 e)None of these

Please give reasons for your answers. And dont read the other comments only after you have put in you answer.

Click Here for answer