Those who matched in 2011 - cyclepsychkal

[ArchivalUser]

0.01(0 + 0.5x98 + 1) = 0.5 or 50%

[ArchivalUser]

@godfather u just dont have common sense.
People like you think too much in life and make simple things complicated

the answer would be 50 % with no exceptions
As the 100th passenger can only and only:::::either
1) sit in his own seat (seat number 100) OR
2) sit anywhere else

I presume he is a human and has only one ass and two gluteals and can only seat in one seat

[ArchivalUser]

@ pinkfloydbeatles

dear sir / madam,

Life is not as simple as you think. And maths too.

What will be ur answer if i ask you the probability of picking 1 white ball from a box containing four balls - 1 white and 3 black balls? I will explain after ur answer.

[ArchivalUser]

If you want to think too much think properly and correctly

Let me give you the right reason why the correct answer is approx 0.5 and not actually 0.5

The whole thing stops when someone else sits in Crazy Guy's seat. The chances of that range from 1/99 (First person) to 1/1 for the last guy. So:

1/99 + Summation from 98 to 2 of ( 1/ n(n+1) )
This returns approximately 0.5 or 50%.

Also, the answer remains approx 50% no matter how many people are added to the line!

[ArchivalUser]

The answer is absolutely 50% and not approximately 50%, whatever the number of total passengers be.

[ArchivalUser]

And the way how you explained the answer to be 50% made no sense at all

"the answer would be 50 % with no exceptions
As the 100th passenger can only and only:::::either
1) sit in his own seat (seat number 100) OR
2) sit anywhere else"

[ArchivalUser]

@ pinkfloydbeatles

The first time you explained your answer to be 50% with a very simple (which can arise only from peanut brains) but a wrong explanation.

The second time you explained all your summations by copying each and every word from the following website ...

"http://www.braingle.com/brainteasers/teaser.php?op=2;id=8903;comm=0"

and just to make yourself sound credible and supreme added that false "approximately" concept.

[ArchivalUser]

Only "peanut brains" think that everything is simple because they can understand only simple things.

[ArchivalUser]

@pinkfloyd & @godfather

your answers are correct, but your explanations are not upto the mark.

@pink - your reasoning is flawed and godfather has given the right example of 1W & 3B balls.
@godfather - you are more closer.

Here is my answer - it is based on Mathematical Induction -- but i will explain in a very intuive way.

1: Say there are only two seats - What is the prob. the second guy sits on his seat 2 if the first guy is crazy? Answer = 1/2 (intuitive).

2: Say there are three seats - What is the prob. the third guy sits on his seat?

Answer = Prob(guy 1 sits on first seat & all is good) + Prob(guy 1 sits on seat 2)*Prob(2) + Prob(guy 1 sits on 3rd seat)*0

Take special note of what I do in second term - I place the first guy in seat 2 and now I have reduced the problem to a problem with 2 guys with one crazy & I know it is 1/2

=1/3 + 1/3*1/2 = 1/2
Prob(3) = 1/2

3: Say there are four seats - what is the prob fourth guy sits on his seat?

Answer = Prob(guy 1 sits on 1st seat) + Prob(guy 1 sits on second seat)*Prob(3) + Prob(guy 1 sits on third seat)*Prob(guy 2 sits on his seat)*Prob(2) + Prob(guy 1 on fourth seat)*0

= 1/4 + 1/4*1/2 + 1/4*1/2
2/4 = 1/2

.....& so on we can prove Prob(100) = 1/2

[ArchivalUser]

Now using the above, we can generalize this for k seats, when 1st guy is crazy, then the chances the kth guy will get seated on his seat will be 1/2

P(2) is true --- the case with two guys
Assume P(k) is true ------- ie with k guys, first crazy, kth guy is in his seat = 1/2
Prove P(k+1) is true or P(k+1) = 1/2

P(k+1) = 1/(k+1) + (k-1)/(k+1)*P(k)
=(k+1)/((k+1)*2)
=1/2

Hence proved for all k