Go Back   GameTavern > House Specials > Happy Hour
Reply
 
Thread Tools Display Modes

How do I solve this?
Old 11-30-2005, 02:16 PM   #1
GameMaster
★★★
 
GameMaster's Avatar
 
GameMaster is offline
Now Playing:
Posts: 14,194
Default How do I solve this?

Aside from my final in two weeks, today hopefully marks the last effing math test I'll ever have to take. Here's a homework problem I can't solve:

1. A group of 30 people is selected at random. What is the probability that at least two of them will have the same birthday?

I think this is kind of how it's supposed to be setup:

n(E') = 365P3 = 365!/(365-30)!

That's as far as I can get. Most calculators can't solve such high numbers.

The answer in the back says: 0.71
  Reply With Quote

Re: How do I solve this?
Old 11-30-2005, 02:34 PM   #2
Dyne
Or should I say.. smanger
 
Dyne's Avatar
 
Dyne is offline
Location: Vancouver
Now Playing: Infinity Blade II, Duke Nukem Forever, Skyrim, Vanquish
Posts: 9,435
Default Re: How do I solve this?

Aha! My Discrete and Combinational Math Teacher just did this yesterday!

We had 23 people in our class, and he said it's a half-half probability that two people had the same birthday.

And two people did. It blew my mind.

As for answering the question, don't use a calculator. Use the computer! I'm very sure that programs called Python or Maple would be able to calculate those.
  Reply With Quote

Re: How do I solve this?
Old 11-30-2005, 02:50 PM   #3
Krypton
Knight
 
Krypton's Avatar
 
Krypton is offline
Location: Michigan
Now Playing:
Posts: 1,427
Default Re: How do I solve this?

good luck!
__________________
  Reply With Quote

Re: How do I solve this?
Old 11-30-2005, 06:23 PM   #4
Canyarion
Nerd of the Rings
 
Canyarion's Avatar
 
Canyarion is offline
Location: insert funny location here
Now Playing: Lotsa games that I need to beat! | WarCraft III + TFT
Posts: 4,638
Default Re: How do I solve this?

Pf, that should be very easy.

First I thought of 30/365, then of 29/365, but none of those were 0.71.

Ok, let's compare it with throwing dice. Let's say you throw a dice 2 times. How big is the chance that at least 2 throws are the same? 1/6. Throw it 3 times: (1/6 +1/6) eeeeeeuh crap, it's 0:30 here, I'm tired and I just had a glass of wine. I don't think it matters what the other rolls(/dates) are once you have 1 the same. So no taurenpoopie of double chances or so to speak.

But that would still bring me to 29/365 = 0.079.

Blast, I should know this.

Edit: I only looked at the chance of the same as the first. It's also the chances of others being the same. So it's 29/365 + 28/365 + 27/365..... = ???

Edit3: I probably made another mistake, because that gives a probability of 1.09 something.
__________________
It may have other powers than just making you vanish when you wish to... The One Ring

"Quotation is a serviceable substitute for wit" - Oscar Wilde

Last edited by Canyarion : 11-30-2005 at 06:33 PM.
  Reply With Quote

Re: How do I solve this?
Old 11-30-2005, 10:48 PM   #5
ZebraRampage
1.618
 
ZebraRampage's Avatar
 
ZebraRampage is offline
Location: Pennsylvania
Now Playing: Borderlands 2
Posts: 2,296
Default Re: How do I solve this?

Quote:
Originally Posted by Dyne
Aha! My Discrete and Combinational Math Teacher just did this yesterday!

We had 23 people in our class, and he said it's a half-half probability that two people had the same birthday.

And two people did. It blew my mind.

As for answering the question, don't use a calculator. Use the computer! I'm very sure that programs called Python or Maple would be able to calculate those.

Maple..
__________________
Wii Code: 8677-2063-2780-3471
SSBB Code: 3136-7083-6578
Mario Kart Code: 4125-0929-1349
  Reply With Quote

Re: How do I solve this?
Old 11-30-2005, 11:28 PM   #6
Neo
Former CEO
 
Neo's Avatar
 
Neo is offline
Location: Longhorn country
Now Playing: Silent Hill: Downpour
Posts: 6,528
Default Re: How do I solve this?

Ignoring the possibility that someone was born on Feb29...


P = (365)(364)(363)....(365 - n + 1)/(365)^n where n = 30.

P = .29368, which is actually the probability that no two people have the same birthday, so

1 - .29368 = .70632 => .71

So in a room with 30 people, chances are more likely than not that two people will have the same birthday. May seem counterintuitive but it's true.
__________________
I write for Cracked. So can you!

Last edited by Neo : 11-30-2005 at 11:37 PM.
  Reply With Quote

Re: How do I solve this?
Old 11-30-2005, 11:29 PM   #7
Neo
Former CEO
 
Neo's Avatar
 
Neo is offline
Location: Longhorn country
Now Playing: Silent Hill: Downpour
Posts: 6,528
Default Re: How do I solve this?

Quote:
Originally Posted by Canyarion
Pf, that should be very easy.

First I thought of 30/365, then of 29/365, but none of those were 0.71.

Ok, let's compare it with throwing dice. Let's say you throw a dice 2 times. How big is the chance that at least 2 throws are the same? 1/6. Throw it 3 times: (1/6 +1/6) eeeeeeuh crap, it's 0:30 here, I'm tired and I just had a glass of wine. I don't think it matters what the other rolls(/dates) are once you have 1 the same. So no taurenpoopie of double chances or so to speak.

But that would still bring me to 29/365 = 0.079.

Blast, I should know this.

Edit: I only looked at the chance of the same as the first. It's also the chances of others being the same. So it's 29/365 + 28/365 + 27/365..... = ???

Edit3: I probably made another mistake, because that gives a probability of 1.09 something.
Don't feel bad, it took mathematicians a long time to figure out how to calculate those kinds of probabilities.
__________________
I write for Cracked. So can you!
  Reply With Quote

Re: How do I solve this?
Old 11-30-2005, 11:42 PM   #8
Yan
Knight
 
Yan's Avatar
 
Yan is offline
Location: Down Under
Now Playing:
Posts: 388
Default Re: How do I solve this?

I hate probabilities I did one semester of Statistics and it neary did my head in, heh.
__________________
post count +1
  Reply With Quote

Re: How do I solve this?
Old 12-01-2005, 12:15 AM   #9
GameMaster
★★★
 
GameMaster's Avatar
 
GameMaster is offline
Now Playing:
Posts: 14,194
Default Re: How do I solve this?

Thanks for the help and encouraging words, my friends. Luckily, there was no problem this challenging on the test. My teacher is cool, he'll teach us the concepts, and then the homework in the math book features normal to difficult problems. And then on the test, he always makes them as simple and straight-forward as possible.
  Reply With Quote

Re: How do I solve this?
Old 12-01-2005, 12:59 AM   #10
Dyne
Or should I say.. smanger
 
Dyne's Avatar
 
Dyne is offline
Location: Vancouver
Now Playing: Infinity Blade II, Duke Nukem Forever, Skyrim, Vanquish
Posts: 9,435
Default Re: How do I solve this?

Quote:
Originally Posted by GameMaster
Thanks for the help and encouraging words, my friends. Luckily, there was no problem this challenging on the test. My teacher is cool, he'll teach us the concepts, and then the homework in the math book features normal to difficult problems. And then on the test, he always makes them as simple and straight-forward as possible.
I wish my Math teachers were like that.

Sigh.
  Reply With Quote
Reply


Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

vB code is On
Smilies are On
[IMG] code is On
HTML code is On
Forum Jump



All times are GMT -4. The time now is 12:42 PM.


vBulletin skin developed by: eXtremepixels
Powered by vBulletin® Version 3.6.4
Copyright ©2000 - 2025, Jelsoft Enterprises Ltd.
GameTavern