The probability that the 2nd chooses a number differendt from the first is
48/49, the probability that the 3rd chooses one different form the two first (given they chose different numbers) is
47/49, so the probability that all 10 choose different numbers is
48x47x...x40 / 49^9
And the probability that at least two numbers are identical is the complement of this.
In R this goes:
> 1 - prod(49-1:9)/(49^9)
[1] 0.6262691
As stated.
Bendix Carstensen
Senior Statistician
Epidemiology
Steno Diabetes Center A/S
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+45 44 43 87 38 (direct)
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> -----Original Message-----
> From: A UK-based worldwide e-mail broadcast system mailing list
> [mailto:[log in to unmask]] On Behalf Of Rodrigo Briceņo
> Sent: 31. december 2012 15:14
> To: [log in to unmask]
> Subject: help understanding an exercise
>
> Dear allstat users. I'm having a hard time trying to understand the logics
> behind the answer of this exercise:
>
> 10 friends choose, on an independent way, a number of the primitive
> lottery (between 1 and 49). The probability that at least 2 of them choose
> the same number is approximately:
>
> And the answer provided is 0.626
>
> I tried with different alternatives but I got different answers.
>
> If someone could help me to understand how to structure the answer that
> will be cool.
>
> --
> Rodrigo Briceņo
> Economist
> [log in to unmask]
> SKYPE: rbriceno1087
>
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