Re: math question verrrrrry off topic
Yes, all true, but for simplicity, since that wasn't crucial to my
argument, I simply repeated this answer already given by two other
people as "close enough" for argument's sake, feeling that the
nuances would simply lose everyone without contributing to the
understanding of what the real problem is with the approach. But
thanks for clarification/correction.
kt
On Jan 19, 2008, at 8:40 AM, Tor-Einar Jarnbjo wrote:
Katharine Thayer schrieb:
Okay, look.
If this were a simple probability experiment, let's say there were
600 objects in a big jar, all exactly the same size and shape and
differing only in color: 450 red ones (for not-accepted) and 150
green ones (for "accepted") all mixed up really well, and the
question was, "if some people from College X reached into the jar
blindfolded and three of them pulled out green objects, what would
the probability of that result be, would it be 1/4x1/4x1/4?" then
the answer would be "only if just three people from College X
reached into the jar. If more than three people from college x
reached into the jar, let's say five people from college x reached
into the jar, then the probability of three of those five people
pulling out a green marble would be 1/4 x 1/4 x 1/4 x 3/4 x 3/4."
That's actually not quite correct either. The simplified solution
of "1/4 x 1/4 x 1/4" for three people drawing is only valid if the
first person puts his object back into the jar before the next
person draws. If the first person keeps the object before the
second person draws, the chance for it to be green (if the first
drawn object was green) is 149/599, which is slightly less than
1/4. The last person would have a chance of 148/598 if both objects
already drawn were green.
The solution "1/4 x 1/4 x 1/4 x 3/4 x 3/4" for a "three out of
five" is also not quite correct, even if you put the objects back
into the jar between each draw. What you get is the probability
that the first three objects are green and that the last two
objects are red. If the order, in which the three green objects are
drawn is insignificant, you have to search deeper in the stochastic
box for a more complicated formula :) You also have to
differentiate between "exactly thee out of five" and "at least
three out of five" green objects. Usually, I would translate the
lack of "exactly" or "at least" in colloquial speech to "at least".
Tor
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