12
   

I Love Solving Math Questions

 
 
markr
 
  1  
Reply Tue 31 Dec, 2013 12:10 am
@tomr,
No.
The probability of at least two people in 366 being born on 2/29 is:
1 - P(0 born on 2/29) - P(exactly 1 born on 2/29) =
1 - (1460/1461)^366 - 366 * (1/1461) * (1460/1461)^365

The probability of exactly two people in 366 being born on 2/29 is:
(366*365/2) * (1/1461)^2 * (1460/1461)^364 / 1461^366
neologist
 
  1  
Reply Tue 31 Dec, 2013 02:25 am
@harpazo,
I just work a daily Sudoku. That way I get to look at numbers without getting involved in their personal problems.
0 Replies
 
raprap
 
  1  
Reply Tue 31 Dec, 2013 02:28 am
@maxdancona,
mea culpa

Birthday Problem

http://upload.wikimedia.org/wikipedia/commons/e/e7/Birthday_Paradox.svg

Rap
0 Replies
 
tomr
 
  1  
Reply Tue 31 Dec, 2013 09:34 am
@markr,
Quote:
No.
The probability of at least two people in 366 being born on 2/29 is:
1 - P(0 born on 2/29) - P(exactly 1 born on 2/29) =
1 - (1460/1461)^366 - 366 * (1/1461) * (1460/1461)^365

The probability of exactly two people in 366 being born on 2/29 is:
(366*365/2) * (1/1461)^2 * (1460/1461)^364 / 1461^366


Thanks, I see now that I had calculated the wrong probability. I now understand the first expression for the probability of 'at least two people born on 2/29'. I do not however understand how you found the second probability of 'exactly two people born on 2/29'. The expression you used looks like [(n(n-1)/2)*(1/d)^2*(d-1/d)^(n-2)]/(d^n) which gives the very very small probability of 1.33e-1160. Because that number is so small I will assume that the expression is (n(n-1)/2)*(1/d)^2*(d-1/d)^[(n-2)/(d^n)] which gives the probability .031 since the last product can be ignored. Did I interpret the order correctly and how did you come to that second expression?
markr
 
  1  
Reply Tue 31 Dec, 2013 11:24 am
@tomr,
I messed up the second one. I'll correct it later.
Romeo Fabulini
 
  1  
Reply Tue 31 Dec, 2013 11:55 am
I just gotta ask this..Smile-
Is there any special significance in the number 666 (the 'number of the beast')?
Do our maths experts see anything out of the ordinary or unusual with that number in any way, mathematically speaking?
tomr
 
  1  
Reply Tue 31 Dec, 2013 11:59 am
@markr,
I think I see what you were doing now. You were using the binomial probability function:

P(x) = (n!/[(n-x)!x!])*(p^x)*(q^(n-x))
where
n-># of trials
x-># of successes (the # of times 2/29 is someones birthday)
p->P(success)
q->P(failure)

So in our example n = 366 x = 2 p = (1/1461)^2 and q = (1460/1461)^364.

P(of exactly 2 people with bdays of 2/29) = (366*365/2)*(1/1461)^2*(1460/1461)^364 = .0243895.

There is a 2.43% chance?
maxdancona
 
  1  
Reply Tue 31 Dec, 2013 12:12 pm
@Romeo Fabulini,
It is the only integer that comes directly after 665.
0 Replies
 
Germlat
 
  1  
Reply Tue 31 Dec, 2013 12:22 pm
@Romeo Fabulini,
Study a little theology and the name of Nero..who doesn't know that?!
0 Replies
 
dalehileman
 
  1  
Reply Tue 31 Dec, 2013 12:41 pm
@harpazo,
I've posed the q #…….709 at various threads with no satisfactory response

Harp it might be that your reluctance to respond is that somehow it makes no logical mathematical sense, in which case, at least, why is that

Or maybe it's a matter of interest: I've submitted many like postings prompting few of any replies. Maybe I'm just not an interesting person

Yet,"Why should there be anything at all" seems the fundamental q

Please advise that my puzzlement entertains a vital q after all and that your delay addressing it owes to need for more lengthy rumination

In any case thanks Harp for volunteering
0 Replies
 
markr
 
  1  
Reply Tue 31 Dec, 2013 01:23 pm
@tomr,
Yep - I threw in an unnecessary division.
0 Replies
 
contrex
 
  1  
Reply Tue 31 Dec, 2013 01:26 pm
@Frank Apisa,
Frank Apisa wrote:
If there are 366 people in the room...there is a 100% chance. Obviously.


Why "obviously"?
Frank Apisa
 
  1  
Reply Tue 31 Dec, 2013 01:30 pm
@contrex,
contrex wrote:

Frank Apisa wrote:
If there are 366 people in the room...there is a 100% chance. Obviously.


Why "obviously"?



Actually, I was wrong.

I meant to write 367. Not sure how I did the 366.

In any case, I stand corrected.

If there are 367 people in the room...the chances of at least two people in the room with the same birthday is 100%.

Obviously.
Romeo Fabulini
 
  1  
Reply Tue 31 Dec, 2013 01:36 pm
Quote:
Germlat said (re the meaning of 666): @RF- :Study a little theology and the name of Nero..who doesn't know that?!

Nah I don't buy the theory that 666 was a 'code' for the Emperor Nero!
For a start, Jesus had no beef with Rome, he even said "pay your taxes to Caesar".
And alhough Rome controlled Israel, they didn't do it in a brutal overbearing way.
So when the disciple John wrote in Revelation ch 13 "This calls for wisdom. Let the person who has insight calculate the number of the beast, for it is the number of a man.That number is 666.",
he probably wasn't referring to Rome or Nero.
In fact it may even have been a prophecy referring to one of our current world leaders or something, but I'm no mathematician which is why 666 means nothing to me.
Germlat
 
  1  
Reply Tue 31 Dec, 2013 01:55 pm
@Romeo Fabulini,
So please explain the "supernatural " principles that affect it.
0 Replies
 
contrex
 
  1  
Reply Tue 31 Dec, 2013 02:03 pm
@Frank Apisa,
Frank Apisa wrote:
If there are 367 people in the room...the chances of at least two people in the room with the same birthday is 100%.


That makes more sense. (For the same reason that if there are 8 people in the room there are bound to be at least two people born on the same day of the week).


0 Replies
 
IRFRANK
 
  1  
Reply Tue 31 Dec, 2013 04:26 pm
@Romeo Fabulini,
Quote:
And alhough Rome controlled Israel, they didn't do it in a brutal overbearing way.


Wow
0 Replies
 
Foofie
 
  1  
Reply Tue 31 Dec, 2013 07:46 pm
@harpazo,
http://math.meetup.com/cities/us/ny/new_york/

This might solve the lonely conern?
0 Replies
 
Romeo Fabulini
 
  1  
Reply Tue 31 Dec, 2013 07:52 pm
Quote:
Romeo said: And alhough Rome controlled Israel, they didn't do it in a brutal overbearing way.
IRFRANK replied: Wow

Yes, Pilate proclaimed Jesus "Not guilty", but the snooty priests overuled him..Smile



Quote:
Germlat said re 666: @RF- So please explain the "supernatural " principles that affect it.

How should I know? That's why I asked our maths experts if there's anything unusual about the number. In fact there are plenty of other numbers in the bible which could also be a sort of "code"..Smile
neologist
 
  1  
Reply Tue 31 Dec, 2013 08:14 pm
@Romeo Fabulini,
Romeo Fabulini wrote:
So when the disciple John wrote in Revelation ch 13 "This calls for wisdom. Let the person who has insight calculate the number of the beast, for it is the number of a man.That number is 666.",
Seven is the number reserved for earthly perfection.
Jesus used repetition for emphasis in Matthew 18: 21:22; Then Peter came up and said to him: “Lord, how many times is my brother to sin against me and am I to forgive him? Up to seven times?” 22 Jesus said to him: “I say to you, not, Up to seven times, but, Up to seventy-seven times
Man falls short of perfection. Hence, 6.
Repetition further emphasizes man's shortcomings as in 666, man's number.
0 Replies
 
 

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