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NNTP-Posting-Date: Tue, 13 Dec 2011 12:20:07 -0600
Message-ID: <4EE79757.5BD4@mindspring.com>
Date: Tue, 13 Dec 2011 13:20:07 -0500
From: pete <pfiland@mindspring.com>
Reply-To: pfiland@mindspring.com
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Subject: Re: Toughest Probability Question
References: <9cb0f967-18d1-410c-9074-f4d84858d9af@u10g2000prl.googlegroups.com> <4EE69C7E.12EB@mindspring.com> <slrnjedm5u.2as3.usenet-nospam@guild.seebs.net> <4EE78837.2A2C@mindspring.com>
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Xref: x330-a1.tempe.blueboxinc.net comp.lang.c:14564

pete wrote:
> 
> Seebs wrote:
> >
> > On 2011-12-13, pete <pfiland@mindspring.com> wrote:
> > > divya bisht wrote:
> > >> How many people must be gathered together in a room,
> > >> before you can be
> > >> certain that there is a greater than 50/50 chance
> > >> that at least two of
> > >> them have the same birthday?
> >
> > >> Discuss Solution in link below
> >
> > > The probability that 23 random birthdays are all different is 0.492703
> >
> > So?
> 
> I made a mistake in the program.

I had it right the first time, 
but I rewrote the whole thing anyway.

/* BEGIN output from new.c */

The probability that out of 23 random birthdays,
that at least two are the same is 0.507297

/* END output from new.c */


/* BEGIN new.c */

#include <stdio.h>

#define YEAR                365  /* 366 */
#define PROB_SOME_SAME      0.5
#define PROB_ALL_DIFFERENT  (1 - PROB_SOME_SAME)

int 
main(void)
{
    int days = YEAR;
    double probability = 1;
    int people = 1;
    puts("\n/* BEGIN output from new.c */\n");
    do {
        ++people;
        --days;
        probability *= 1.0 * days / YEAR;
    } while(probability > PROB_ALL_DIFFERENT);
    printf("The probability that out of %d "
        "random birthdays,\n"
        "that at least two are the same is %f\n", 
        people, 1 - probability);
    puts("\n/* END output from new.c */");
    return 0;
}

/* END new.c */


-- 
pete