Posted by Case in point --ros on March 21, 1999 at 13:30:51 {MWiPgYg2nZn0g}:
In Reply to: ******Evolutionism and Creationism posted by 5GJW on March 21, 1999 at 11:32:05:
Thanks for illustrating the point so well, 5GJW. :)
It is also commonly observed that many people who are apt in math, are more challenged by grammar, and vice-versa. You said:
This is the definition of probability, applied to this
question. As it is the definition, there is no proof, we simply said that this is what it
means.
Wrong, we said this was "given"; in other words, absolute--not probability nor "what it means." There is proof in the self-evident. There is proof to anyone who can see it, like seeing green if you are not color-blind; but the proof cannot be demonstrated mathematically--at least according to that math instructor.
Given:
There is a set of 100
people.
All are either JW or Catholic(J or C)
There is at least one J and at least one C.
In any 2 samples of the set, the probability of at least 1*C is equal to 1 ( P(C) = 1).
This can be rephrased as the probability of 2*J
= 0 (P(2J)=0)
You have incorrectly restated the premises. Probability is Not the issue; possibility is. If there were even only two JWs in the group of 100 people, the probability of them being paired certainly would be very low--but possible and therefore the statement (as I stated it, not as you did) that:
In ANY combination of two people, at least one is Catholic
You said:
These events
are not mutually exclusive, the first selection changes the probability of the second selection.
Wrong again. The first statement by itself could mean that all are C or all are J. The second statement simply eliminates this as a possibility--a necessary component for the puzzle.
If we select one element from the set, the probability of selecting a J = (Number of Js in Set)/(Size of set).
The probability of 2*J can be expressed as P(2J) = ((Number of Js)/(100)) * (Number of Js - 1)/(99)).
Except, as stated, you have introduced the component of "probability" which has no place in this puzzle. And you don't have any basis for the above equation of "probability of 2J or Number of Js -1/99 from the original problem. Your equation makes no sense for solving the problem. That's because you were right in the first place. Its not provable mathematically.
In order for P(2J) = zero to be true, Number of Js = 0 or 1. As it is given that there is at least 1 J, 1 is the correct answer.
Except you do not have a basis for concluding P (2J) to begin with. If you have 2 JWs, you could as well have P(10J), P(20J) or P(30J) or any number between P(2J) to P(50J). (Plus you just demonstrated that the first two statements are not mutually exclusive.)
5GJW, with textbook in hand
I rest my case (or maybe I should say, the math instructor's case). :)
Anyway, now I'll present one that is more challenging for "abstract reason"ers, but one that IS solvable by algebria. You might get this one, 5GJW. However, if J.H. is particularly good at so-called "right-brain" "abstract reasoning", he might get it before the mathematician. I'm going to post it at the top incase people are not reading down this far.
Ros