# Typical Interview Question

_There are 3 stations A, B and C. Trains leave from A to C and from C to A at regular intervals. A guy at B boards any train that comes to B at any time of the day and heads to either A or C. But on analysis it was found out that 75% of the time h…

There are 3 stations A, B and C. Trains leave from A to C and from C to A at regular intervals. A guy at B boards any train that comes to B at any time of the day and heads to either A or C. But on analysis it was found out that 75% of the time he lands at A and only 25% of the time he lands at C. What could have been the reason.
There is no trick in the question. The station is MIDWAY between A and C and there are an infinite number of trains at REGULAR intervals between A and C.
Totally confusing?? :huh:
Ketan
PS: I do not know the answer
PS1: This was asked in one of the ISB interviews
There are 3 stations A, B and C. Trains leave from A to C and from C to A at regular intervals. A guy at B boards any train that comes to B at any time of the day and heads to either A or C. But on analysis it was found out that 75% of the time he lands at A and only 25% of the time he lands at C. What could have been the reason.
There is no trick in the question. The station is MIDWAY between A and C and there are an infinite number of trains at REGULAR intervals between A and C.
Totally confusing?? :huh:
Ketan
PS: I do not know the answer
PS1: This was asked in one of the ISB interviews

Its simple i guess....
The number of trains running from A to C are 3 times as compared to number of trains running from C to A in a day pal.....

Let me know in case i missed some point....

Regards
Mohit

this can be possiblity

since the trains are of regular intervals, trains going to A should come every four min...and trains towards b should come every 5 min(considering that if a train towards A comes at 10 then train towards B should come at 10.01...) so the probability that a person land with train B is very less....and hence the percentage...

this could be a possiblity...but not sure...maybe the question is only to judge how u apply ur thoughts....

the train

There are 3 stations A, B and C. Trains leave from A to C and from C to A at regular intervals. A guy at B boards any train that comes to B at any time of the day and heads to either A or C. But on analysis it was found out that 75% of the time he lands at A and only 25% of the time he lands at C. What could have been the reason.
There is no trick in the question. The station is MIDWAY between A and C and there are an infinite number of trains at REGULAR intervals between A and C.
Totally confusing?? :huh:
Ketan
PS: I do not know the answer
PS1: This was asked in one of the ISB interviews

Hey Ketan,

First train from both A and C leaves at 6.00
Let us assume that train from station A takes 60 min. to reach station B and each subsequent train leaves from A at an interval of 60 min.So trains from sation A would reach B at 7.00,8.00,9.00 and so on
Now assume that train from station C takes 19 min. to reach staion B and each train thereafter leaves at an interval of 20 min.So trains from C would reach B at 6.19,6.39,6.59,7.19,7.39,7.59 and so on.

Cleary in between 6.00 and 7.00 and for each subsequent hour ,a guy would board train from C to A at B at 6.19,6.39 and 6.59 and in opposite direction at 7.00.
Out of 4 times in an hour,3 times he reaches A and ones C.So we get 75% and 25% keeping all the questions stipulations in mind.

Hope have not missed any detail.

Basically its same as saying trains from C runs 3 times in no. to trains from A as someone posted but, only a detailed analysis.
Just following wht corporate world has tought me,to complicate things when they are simple.

Peace.
Some of the possible answers quoted by people. Do not blame if any or all answers sound weired......... I dont know the answer....
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Its either distance or speed that needs to be skewed in one direction for you to arrive at a particular destination more often. If you state something I can assume ... provided of course it is mentioned clearly.
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The question that probably needs to be answered is
What is the probability at each instant of B having an A bound train and
what is the probability of B having a C bound train.
Now what factors can influence this probability
(i)Frequency of the trains(Ruled out, because they have the same
frequency)
(ii)Speed of the trains(Ruled out, because the trains have fixed
frequencies on both sides)
The only problem that I see here is the averaging cycle. Even a unbiased
coin has to tossed a large number of times to get a perfect 0.5
experimental probability of heads and tails. If the observation period
was not long enough, then you may get biased results.
I hope I am making sense.
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My take on the trains question:
If you toss a coin, the prob of H or T is 0.5, but
that is the prob for an infinite number of tosses. The
distribution curve for a finite number of events is
not normal - the lower the # of events, the less
normal it can be.
Right now, I just tossed a coin 10 times and came up
with: # of heads = 4, # of tails = 6. I have tossed
the coin 5 times again now and now have 4 tails and 1
head. Hey, why is my coin favoring tails! - so I toss
it again 5 times and it now is 3 heads and 2 tails. So
one reason for the guy landing on A 75% of the time
could be that # of events was low.
===========================================================
Step 1: It is possible that the sample size is small - for a 5% error
and 95% confidence, the sample size should be at least 384, and for
2% error & 99% confidence it should be 4160
(http://www.surveyguy.com/SGcalc.htm)
Step 2: If the sample size is indeed greater than 4160, then it is
possible that there is a bias. What that is, could be that the guy
comes to station B everyday and our experiment says that after 4160
days we finds he lands on A 75% times. It is possible that he usually
watches Noddy on Pogo everyday before leaving for the station, and at
that time, normally a train towards A comes... or whatever.
Step 3: If this too is not the case, then what we could have
encountered is Type 1 error. Its a chance, but can happen in real
world (http://www.isixsigma.com/offsite.asp?
A=Fr&Url;=http://www.intuitor.com/statistics/T1T2Errors.html)
Unless there was something else to the question.
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Or maybe..after some trips, the route to C gets blocked..one of the trains break dn or smthng..and so most trains to C get cancelled anyway..and the guy boards train/s to A!
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Maybe some trains never reach B, so of 150 trains
sample, 75 reach A and only 25 reach B: the remaining
50 intented towards B do not reach B because of the
fault ... or the railroad person is sleepy too and
ends up directing some trains to D! :smile:
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75% of trains from C to A stops at station B and only 25% of trains from A
to C stops at station B.
===========================================================
timings musta been
Train to A - 12:00
Train to C -12:01
Train to A - 12:10
Train to C - 12:11
....so on
So if the guy was in the station B at any time bet
12:00 and 12:01(1 minute) he 'd go to C
But if he were there bet 12:01 and 12:10(9 minutes)
he'd go to A
So that way the prob of goin to A wud b 9 times tht of
C
Only tht here coz Manu said 1:3 we'll have to use app
times to get the 4 as base
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hey ppl, I have a totally different viewpoint here....I may be completely off target so please pardon me if you find this stupid.
Maybe there are 2 platforms at station B.
Platform 1: trains only go towards A
Platform 2: trains only go towards C
75% of the time this guy happens to be at platform 1. Thats why!!!

well i see it in a personal view
if i m going to station A 75% of time then it is clear that the trains r not at regular interval.
or if there r then i m finding easier to board on the trains which r going towords A. i mean to say
1] Availability of these trains r higher... or
2] it is easier to board on the trains which r going towords A like Plateform as one already said. Another thing can be that as i am going to station B then it may be a perticuler time and at that time probability of getting train for A is higher than C.
So it's mine view but don't laugh at me......

There are 3 stations A, B and C. Trains leave from A to C and from C to A at regular intervals. A guy at B boards any train that comes to B at any time of the day and heads to either A or C. But on analysis it was found out that 75% of the time he lands at A and only 25% of the time he lands at C. What could have been the reason.
There is no trick in the question. The station is MIDWAY between A and C and there are an infinite number of trains at REGULAR intervals between A and C.
Totally confusing?? :huh:
Ketan
PS: I do not know the answer
PS1: This was asked in one of the ISB interviews

Can it just be the stoppage time of the trains going to the station with the higher chance stops at station b for a greater percentage of time..I m no great probability guy .so I dont know if this is correct