Romeo & Juliet meetup
Moderators: jestingrabbit, Moderators General, Prelates
 fjafjan
 THE fjafjan
 Posts: 4766
 Joined: Fri Oct 06, 2006 12:22 pm UTC
 Location: Down south up north in the west of eastern west.
 Contact:
Romeo & Juliet meetup
Okey so I might mix up some minor detail but I believe the problem is as such (and if there uncertainties do ask)
Romeo and Juliet are to meet in the town square, but they cannot decide a fixed time because then they will get caught. So they have decided to meet sometime between 23.00 and 00.00 but neither party knows when the other will arrive. Because they don't want to get caught they will only stay at the town square for ten minutes, and they will always leave when the clock strikes 00.00. They will always arrive at a "full minute" ie they will not arrive 23:45.23.
If one party is leaving the same minute another is arriving they will meet.
What is the probability Romeo and Juliet will meet?
I solved this problem (I thought) but was told my answer was incorrect, so I might as well let you guys go at it first and then I will say what I think is the right answer and what is supposedly the right answer.
Romeo and Juliet are to meet in the town square, but they cannot decide a fixed time because then they will get caught. So they have decided to meet sometime between 23.00 and 00.00 but neither party knows when the other will arrive. Because they don't want to get caught they will only stay at the town square for ten minutes, and they will always leave when the clock strikes 00.00. They will always arrive at a "full minute" ie they will not arrive 23:45.23.
If one party is leaving the same minute another is arriving they will meet.
What is the probability Romeo and Juliet will meet?
I solved this problem (I thought) but was told my answer was incorrect, so I might as well let you guys go at it first and then I will say what I think is the right answer and what is supposedly the right answer.
//Yepp, THE fjafjan (who's THE fjafjan?)
Liza wrote:Fjafjan, your hair is so lovely that I want to go to Sweden, collect the bit you cut off in your latest haircut and keep it in my room, and smell it. And eventually use it to complete my shrine dedicated to you.
 skeptical scientist
 closedminded spiritualist
 Posts: 6142
 Joined: Tue Nov 28, 2006 6:09 am UTC
 Location: San Francisco
Re: Romeo & Juliet meetup
Assuming each decides independently on a random time between 11:00 and 11:59 to arrive, and if one arrives at the exact instant the other leaves then they fail to meet,
Spoiler:
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.
"With math, all things are possible." —Rebecca Watson
"With math, all things are possible." —Rebecca Watson
Re: Romeo & Juliet meetup
Skep, one of your assumptions is not based on the OP.
I also assumed that it was possible to arrive at 00:00 and if the other is there meet, otherwise immediately leave.
What answer were you told Fja?
Joke answer:
fjafjan wrote:If one party is leaving the same minute another is arriving they will meet.
I also assumed that it was possible to arrive at 00:00 and if the other is there meet, otherwise immediately leave.
Spoiler:
What answer were you told Fja?
Joke answer:
Spoiler:
"Everything I need to know about parenting I learned from cooking. Don't be afraid to experiment, and eat your mistakes."  Cronos
 skeptical scientist
 closedminded spiritualist
 Posts: 6142
 Joined: Tue Nov 28, 2006 6:09 am UTC
 Location: San Francisco
Re: Romeo & Juliet meetup
I prefer my assumptions as they lead to a simpler answer. In any case, the solution method will be the same.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.
"With math, all things are possible." —Rebecca Watson
"With math, all things are possible." —Rebecca Watson
 fjafjan
 THE fjafjan
 Posts: 4766
 Joined: Fri Oct 06, 2006 12:22 pm UTC
 Location: Down south up north in the west of eastern west.
 Contact:
Re: Romeo & Juliet meetup
Yeah you guys had the same solution as me, where I assumed the max of 20 minutes. the 'correct' answer was supposedly 1/36 if you drew a graph and calculated the area under it (trying to aquire it atm). This problem was a problem for my little sister so when I solved it I figured
A the answer was (as you said) 'clunky'
B a bit too hard for a 9th grader (but not extremly)
So yeah, I too arrived at first two sums of 10/60+11/60...19/60, then one sum of 40*20/60 for the "middle" times, all multiplied by 1/60, so I got some ugly fraction.
A the answer was (as you said) 'clunky'
B a bit too hard for a 9th grader (but not extremly)
So yeah, I too arrived at first two sums of 10/60+11/60...19/60, then one sum of 40*20/60 for the "middle" times, all multiplied by 1/60, so I got some ugly fraction.
//Yepp, THE fjafjan (who's THE fjafjan?)
Liza wrote:Fjafjan, your hair is so lovely that I want to go to Sweden, collect the bit you cut off in your latest haircut and keep it in my room, and smell it. And eventually use it to complete my shrine dedicated to you.
 Kingreaper
 Posts: 170
 Joined: Sun Jan 27, 2008 4:23 pm UTC
Re: Romeo & Juliet meetup
[quote="fjafjan"]Yeah you guys had the same solution as me, where I assumed the max of 20 minutes. the 'correct' answer was supposedly 1/36quote]
If they always arrived at a precise ten minute interval, ie. 11:00, 11:10, 11:20 etc. and only met if they arrived at the same one, the answer would still be 1/6. 1/7 if you include arriving at precisely midnight as an option.
And that's discounting the possibilities of overlapping times which increase the probability of their meeting for obvious reasons.
How on earth the "correct" answer is lower probability than that scenario I cannot fathom. Let alone 1/36
If they always arrived at a precise ten minute interval, ie. 11:00, 11:10, 11:20 etc. and only met if they arrived at the same one, the answer would still be 1/6. 1/7 if you include arriving at precisely midnight as an option.
And that's discounting the possibilities of overlapping times which increase the probability of their meeting for obvious reasons.
How on earth the "correct" answer is lower probability than that scenario I cannot fathom. Let alone 1/36
Re: Romeo & Juliet meetup
The answer in the continuous case is 11/36, not 1/36.
 jestingrabbit
 Factoids are just Datas that haven't grown up yet
 Posts: 5967
 Joined: Tue Nov 28, 2006 9:50 pm UTC
 Location: Sydney
Re: Romeo & Juliet meetup
fjafjan wrote:1/36
I don't know what's right, but that is incredibly wrong. I would suggest that your sister propose a wager to the teacher. Not only will she make some money, but someone that far off should receive some sort of humiliation if they're going to teach that wrongness to others.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.
 skeptical scientist
 closedminded spiritualist
 Posts: 6142
 Joined: Tue Nov 28, 2006 6:09 am UTC
 Location: San Francisco
Re: Romeo & Juliet meetup
I'm guessing he meant 11/36. In any case, the problem specifically stated that they always arrive at multiples of one minute, so the continuous case answer is just wrong for the problem as stated.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.
"With math, all things are possible." —Rebecca Watson
"With math, all things are possible." —Rebecca Watson
 fjafjan
 THE fjafjan
 Posts: 4766
 Joined: Fri Oct 06, 2006 12:22 pm UTC
 Location: Down south up north in the west of eastern west.
 Contact:
Re: Romeo & Juliet meetup
Nitrodon wrote:The answer in the continuous case is 11/36, not 1/36.
Ah! I might have misstated and this was the given answer (It was my first suspicion that the correct answer was just the same question in the continuous form but because I was told it was incorrect at a dinner party I couldn't bring out pen paper and solve it... Still, the question was not asked in for the continuous case but either 1 or 10 minutes arrival possibilities.
//Yepp, THE fjafjan (who's THE fjafjan?)
Liza wrote:Fjafjan, your hair is so lovely that I want to go to Sweden, collect the bit you cut off in your latest haircut and keep it in my room, and smell it. And eventually use it to complete my shrine dedicated to you.

 Posts: 26
 Joined: Mon Nov 09, 2009 8:49 am UTC
Re: Romeo & Juliet meetup
Do we assume that Romeo & Juliet are intelligent and logical people? (given they will both kill themselves in a couple of days time this may not be a valid assumption).
Juliet can rationalise that it would be foolish to arrive at minute 5 for example. She would then only see Romeo if he arrived at minute 015. Juliet could realise she would be better to arrive at minute 10 than minute 5, as she would still see Romeo if he arrived at minute 015, but would also see him if he arrived at minutes 1620.
Using this (or similar) logic, neither Romeo or Juliet will arrive in the first 10 or final 10 minutes of the hour. I will leave someone else to do the maths, but this will increase the probability, would it not?
As an aside, if this were done as an experiment with 1000 pairs of people, I would expect most to lob between about minutes 2040 and the number of pairs that would meet would be somewhere near 500, possiblity higher.
Juliet can rationalise that it would be foolish to arrive at minute 5 for example. She would then only see Romeo if he arrived at minute 015. Juliet could realise she would be better to arrive at minute 10 than minute 5, as she would still see Romeo if he arrived at minute 015, but would also see him if he arrived at minutes 1620.
Using this (or similar) logic, neither Romeo or Juliet will arrive in the first 10 or final 10 minutes of the hour. I will leave someone else to do the maths, but this will increase the probability, would it not?
As an aside, if this were done as an experiment with 1000 pairs of people, I would expect most to lob between about minutes 2040 and the number of pairs that would meet would be somewhere near 500, possiblity higher.
Re: Romeo & Juliet meetup
You've also got to factor in that they're both young and flighty (so may well be running later than they planned) and desperately in love (so might hurry to get there early). Perhaps those factors cancel out?
 TheChewanater
 Posts: 1279
 Joined: Sat Aug 08, 2009 5:24 am UTC
 Location: lol why am I still wearing a Santa suit?
Re: Romeo & Juliet meetup
Serious:
Joke:
Spoiler:
Joke:
Spoiler:
http://internetometer.com/give/4279
No one can agree how to count how many types of people there are. You could ask two people and get 10 different answers.

 Posts: 3
 Joined: Wed Dec 30, 2009 6:08 am UTC
Re: Romeo & Juliet meetup
Since there are a relatively small number of cases, I just wrote a quick java program to test each one.
Spoiler:
 TheChewanater
 Posts: 1279
 Joined: Sat Aug 08, 2009 5:24 am UTC
 Location: lol why am I still wearing a Santa suit?
Re: Romeo & Juliet meetup
BoFairfield wrote:I don't know the syntax of loops in Python.[/spoiler]
Ah, I think you're right. I don't know exactly how loops work in Python either, which might explain why I got a different answer in C++. Although, I did do it much differently.
Spoiler:
http://internetometer.com/give/4279
No one can agree how to count how many types of people there are. You could ask two people and get 10 different answers.

 Posts: 3
 Joined: Wed Dec 30, 2009 6:08 am UTC
Re: Romeo & Juliet meetup
you got 1150/3600, which is because your for loops don't include midnight, whereas I got 1171/3721 because mine do. The OP doesn't specify which way is correct, but it's just a difference of <= vs < in the for loop headers
Who is online
Users browsing this forum: No registered users and 11 guests