Re: [Phys-L] From a Math Prof (physics BS major) at my institution ( math challenge)

[Jeffrey Schnick <JSchnick@Anselm.Edu>]

> -----Original Message-----
> From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Craig Wiegert
> Sent: Wednesday, February 26, 2014 2:38 PM
> To: Phys-L@Phys-L.org
> Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my institution (
> math challenge)
>
> It doesn't matter, aside from efficiency.
Agreed.
...
> If I put 6 numbers in a hat and draw two without replacement, then there are
> 30 equally likely outcomes (preserving the order of the numbers that are
> picked).
>
> Now let's say I put 6 numbers in a hat and draw two *with* replacement, but
> with the condition that if the second draw is the same number as the first, I
> put it back and redo my second draw until I get a different result.  Let's
> calculate the probability that the two numbers end up being "1" and "2", in
> that order.  Well, the first draw picks "1" with probability 1/6.  The second
> draw picks "2" 1/6 of the time... or "1" 1/6 of the time, in which case I redo.
> That redo similarly picks "2" 1/6 of the time, or "1" 1/6 of the time which
> would mean *another* redo, and so on.
>
> The probability that the second draw ends up being "2" after as many redos
> as it takes is
> 1/6 (zero redos) + 1/36 (one redo) + 1/216 (two redos) + ... = 1/5.
> So the overall chance of picking "1" and then "2" is 1/30.  Aside from being
> distinct, "1" and "2" aren't special, thus all of the ordered pairs of distinct
> numbers occur with equal probability 1/30.
>
> I'm by no means proficient in matlab/octave, but it seems like all of this
> choosing code could be replaced with calls to randperm(35, 5).
Nice suggestion.  I'll try that if I continue to play with it.
...