Tricky Puzzle : Trains Every 10 minutes || Logic + Math

Tricky puzzle based on Logic and Math:
John lives near the city center railway station (C).
He has two friends Tony and Carl...living near the West terminal and the east terminal railway stations respectively (shown as X and Y).
Every day... John travels by train to meet one of his friends (that's either Tony or Carl).
He reaches station C at a random time everyday... and takes the first available train.
- From Station C, Trains going towards station X are scheduled every 10 minutes.
- Also... From Station C,trains going towards station Y are scheduled every 10 minutes.
That means, the frequency of trains going from C to X is exactly same as the frequency of trains going from C to Y...
But Five out of 6 times, John meets Tony!
Can you explain why does the meeting probability favors Tony ?
Pause the video.... think logically and think mathematically.

It's a very tricky math riddle that involves logic and math. You must try this tricky math puzzle by yourself.
This puzzle is sometimes asked in software interviews.
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Logically Yours is a channel intended to share the explanation of har and tricky puzzles, riddles and brainteasers.

Please give a try to previous versions of interview riddles episodes.

10 Interview RIDDLES || Episode #4 || Quick & Tricky

5 Interview RIDDLES || Episode #5 || Presence of mind

10 Interview RIDDLES || Episode #3 || Intelligence Test

10 Interview RIDDLES || Episode #1 || Frequently asked Job Interview RIDDLES

5 Interview PUZZLES || Episode #2 || Frequently asked Job Interview PUZZLES

[mrropek]

I'm really want to know how john comes back to his house, walking? What a day😁

[hemrajphagna]

Start train to Y at 8 then chances of meeting to Carl favors more. U should have asked Q in another way.

[cricketcoachingforchildren]

The explanation is superb. Mathematicians and Statisticians will appreciate
your explanation but others
may not have patience to
go through the entire video.
Please include chess board
puzzle as soon as possible.

[jaideepbanerjee]

Very nice puzzle. The puzzle never said that John will meet Tony 5 out of 6 times under every condition. It asked if John meets Tony 5 out of 6 times, what would be the condition.This probability is possible only when the train to station Y starts 100 sec after train to station X. This also means that if the time difference is changed from 100 sec then the probabilty will also change. Alternatively if this time difference is 500 secs then John will meet Carl 5 out of 6 times

[christianfunintuscany]

I tried to solve this very interesting puzzle but I could not find the solution, I tried to search for something capable to turn the 1/2 1/2 probability into the 1/6 5/6 one, that’s an independent event, but I reached nowhere :( it is impressive that from the relative chance to meet two persons it is possible to deduce the timetable of the trains! Cool!

[kunalbatham]

Question : why does the meeting probability favors Tony ? 🧐
Is a wrong question here, because we don't know what you are exactly asking about .
Your question should be : in what conditions is this possible ? 🤔
Then we can think and apply our mind for the timings of train should be like

[nandapeela]

Again you are the best..
Pls make videos frequently.
Please notice that logically yours have many fans and always wishes a notification from amer.. 😊😊

[TheJackal]

WOW, man! Long time! Can't believe you still around.

[wernerviehhauser]

The solution is obvious for someone who has paid attention to the time tables of public transportation :-)

[chinmoyrajdeka]

You have assumed Train from C to X starts first. But its not mentioned anywhere. So what if Train from C to Y starts first? Then John would meet Carl 5 out of 6 times.. So the concept is not solid..

[sachinkumarbit]

Wrong we can take Ty then it will reverse....

[jessicataylor]

Great puzzle! Where is this weird place that schedules trains to the second and people base meet ups on the first train available? Bonus question for extra credit: Take the frequency of disappointment, add the intensity of frustration, multiply by the time wasted and tears spilled while waiting at platform Y, to calculate the probability of Carl deciding not to bother with John. Think logically 😉😂

[SaurabhYadav-ystm]

Now I have become puzzle solver after solving too many puzzles available on your channel

[rameshkiran]

Cracked it just under a minute, directly thought 5:1 of 600

[namratawedding]

What if train for x is scheduled for 8:00 but for y its 8:09 then probability of getting to y is 0.9 in 10 minutes. So its only dependent on diff between first train timing.

[yuvrajdeore]

That means chances to reach exactly @8:00 or after 8:02 are more than reacing between 8:00 to 8:01:40 ..

[vinaysaxena]

Nice. But I have a clarification. It is that we do not know which train is first to leave from station C. And what if the time difference between two trains is exactly 5 minutes?

[TheRnsrns]

I think there's a critical assumption here which you forgot to mention, wich is, Train Leaving station X is scheduled earlier than train leaving for station Y. Your explanation would be completely reversed if you start assuming that train to station Y leaves at 8 am and Train to station X leaves 2 min after that at 8 02 am. In that case, he'll be meeting Carl 5 times of 6.

[neteesan]

I thought He was lazy to cross the train track and to catch a train to meet carl.. lol.. is it not logical?

[kareemahmed]

It depends only on his arrival time; and the two trains are not leaving simultaneously; there is two minute between them