U of S | Mailing List Archive | alt-photo-process-l | Re: math question verrrrrry off topic

Re: math question verrrrrry off topic

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".