Re: A problem for complete beginners

"Luis A. Afonso" wrote:
> I proposed this problem in order to make clear what is a sample with replacement and without replacement. These are simple concepts but even so confusing for some people.

I was actually going to post an answer to this, but other pressing
things kept coming up.

I was a bit confused about the language of the original question. I
would have thought that putting the drawn cards "on the bottom of the
pack" was a bit clearer as the word "in" suggests "inside". I assumed
that you meant samping without replacement (due to the size of the pack
and the small number sampled), as you later confirmed. The probability
of various numbers of black cards in the first three cards sampled will
follow a hypergeometric distribution with n=26, m=26, and k=3, no?

Here's something that I at least find an interesting consequence of
your problem. If we don't look at the first card that is drawn, then
the probability of the second card drawn being black is still 0.5.
Similarly if we don't look at the first two cards drawn, then the
probability of the third card being drawn being black is still 0.5.
Now, if we were sampling with replacement (i.e. binomial) the
probability of a black card would be 0.5 each time. So, if I mistakenly
claimed that the hypergeometric and binomial probabilities of getting 2
black cards out of 3 sampled should be the same, why would I be wrong?
:-)

Cheers,

Ross-c

.

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