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(42S) Probability of Same Birthday Day
12-05-2018, 06:09 PM
Post: #1
(42S) Probability of Same Birthday Day
Mini Program: Probability of Same Birthday Day
by Guillermo Castarés
Dic-2018

Given a group of n people, what is the probability that at least two of them share the birthday day?

Takes n from register X and put result on the same register.

Important program to have if you like to bet ;-)

Stack not preserved.

No flags and data registers used.


Examples of use:

10 [Psbd]
0.1169

23 [Psbd]
0.5073

25 [Psbd]
0.5687

50 [Psbd]
0.9704

70 [Psbd]
0.9992

Code:

00 { 32-Byte Prgm }
01>LBL "Psbd"
02 1
03>LBL 00
04 366
05 RCL- ST Z
06 365
07 ÷
08 ×
09 DSE ST Y
10 GTO 00
11 1
12 X<>Y
13 -
14 END

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12-05-2018, 08:36 PM
Post: #2
RE: (42S) Probability of Same Birthday Day
(12-05-2018 06:09 PM)morex Wrote:  Given a group of n people, what is the probability that at least two of them share the birthday day?

What about a direct solution?

Code:
00 { 26-Byte Prgm }
01>LBL "BDAY"
02 365
03 X<>Y
04 PERM
05 365
06 LASTX
07 Y^X
08 ÷
09 1
10 X<>Y
11 -
12 END

Yes, on a real hardware 42s this will overflow for n > 195. Unlike your program that shoud be able to handle such cases.
But then... for n ≥ 135 the 12-digit result is 1 anyway. ;-)

Dieter
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12-05-2018, 09:02 PM
Post: #3
RE: (42S) Probability of Same Birthday Day
(12-05-2018 08:36 PM)Dieter Wrote:  What about a direct solution?

Yes, on a real hardware 42s this will overflow for n > 195. Unlike your program that shoud be able to handle such cases.
But then... for n ≥ 135 the 12-digit result is 1 anyway. ;-)

Dieter

Nice. Thanks!

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12-05-2018, 11:46 PM (This post was last modified: 12-05-2018 11:46 PM by ijabbott.)
Post: #4
RE: (42S) Probability of Same Birthday Day
The generalised birthday problem (probability of at least n people in a group sharing a birthday) is a lot harder. Probably intractable on a HP-42S. (Now there's a challenge!)

— Ian Abbott
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12-06-2018, 04:32 AM
Post: #5
RE: (42S) Probability of Same Birthday Day
(12-05-2018 11:46 PM)ijabbott Wrote:  The generalised birthday problem (probability of at least n people in a group sharing a birthday) is a lot harder. Probably intractable on a HP-42S. (Now there's a challenge!)

Intractable on a 42S?

Birthday problem generalizations

V.
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12-06-2018, 05:54 AM
Post: #6
RE: (42S) Probability of Same Birthday Day
(12-06-2018 04:32 AM)Valentin Albillo Wrote:  Birthday problem generalizations

The probability of being born on February 29th is NOT zero. The above document seems to utterly ignore leap year babies.

X<> c
-Joe-
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12-06-2018, 08:49 AM
Post: #7
RE: (42S) Probability of Same Birthday Day
(12-06-2018 04:32 AM)Valentin Albillo Wrote:  
(12-05-2018 11:46 PM)ijabbott Wrote:  The generalised birthday problem (probability of at least n people in a group sharing a birthday) is a lot harder. Probably intractable on a HP-42S. (Now there's a challenge!)

Intractable on a 42S?

Birthday problem generalizations

V.

Specifically, the Multiple Birthday Problem. You may be able to get approximate results (up to about 3 decimal places) using Levin's approach mentioned in that paper, but a combinatorial approach blows up too quickly as n increases, rendering it unsuitable for computation on a HP 42S.

I did knock up a program in C++ (but really C style but using C++ for convenence) using the GNU Multiple Precision library (which is a PITA to use in C, hence the use of C++ for convenience) to generate exact probabilities a while ago, although I'm not proud of it as the calculations are far from optimal (too many repeated sub calculations). Anyway, here is is: ian-abbott/birthdays.cpp (raw).

(12-06-2018 05:54 AM)Joe Horn Wrote:  The probability of being born on February 29th is NOT zero. The above document seems to utterly ignore leap year babies.

Assume a spherical cow. Smile

— Ian Abbott
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12-06-2018, 03:59 PM
Post: #8
RE: (42S) Probability of Same Birthday Day
(12-06-2018 05:54 AM)Joe Horn Wrote:  The probability of being born on February 29th is NOT zero.

Of course it's not zero (0.00068 > 0), no one would say it is so no need to highlight the "NOT", everybody knows that.

Quote:The above document seems to utterly ignore leap year babies.

Me too, I've never met anybody born on that date. Smile

V.
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12-06-2018, 07:49 PM
Post: #9
RE: (42S) Probability of Same Birthday Day
Quote:Me too, I've never met anybody born on that date. Smile

Superman! :-)

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12-10-2018, 05:10 PM (This post was last modified: 12-10-2018 05:46 PM by Joe Horn.)
Post: #10
RE: (42S) Probability of Same Birthday Day
(12-06-2018 03:59 PM)Valentin Albillo Wrote:  
(12-06-2018 05:54 AM)Joe Horn Wrote:  The probability of being born on February 29th is NOT zero.

Of course it's not zero (0.00068 > 0), no one would say it is so no need to highlight the "NOT", everybody knows that.

I was NOT highlighting it; I was following HP Prime syntax, which insists on NOT being capitalized. Big Grin

[Image: not0b.png]

EDIT: Come to think of it, here's a mini-challenge for ya: Write a program for the Same Birthday Probability problem, taking leap years into account.

EDIT 2: Never mind, the following delightful article fully explains the solution and its impact on the probabilities, which (as everybody said above) is minimal.
http://www.efgh.com/math/birthday.htm

X<> c
-Joe-
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