I can TELL myself all this: On Sat, Oct 27, 2012 at 2:15 PM, Landon Hurley <[email protected]> wrote: >> > > The probability that you will or will not roll a 1 is .5. The > probability that the roll will result in a 1 is 1 in 6, given the event > that you have rolled a six sided die. You can reduce most events to will > or will not happen. That isn't the true representation of that scenario > though. > > It can only be .5 if there are two equally probable events. How you are > presenting them is not in terms of the probability of those outcomes, > but in that given two discrete categories (1 or 2,3,4,5,6) the > probability is .5 that you will land on 1. > > The inverse of rolling a one is important as well. The probability of > rolling a 2 must also be .5, according to your interpretation. But since > all possible probabilities must sum to 1, .5(6)=3 (or .5 added for each > of the six possible events) is a contradiction, not to mention > impossible given that probability is a continuum from 0 to 1. > > Given your terms: > In terms of a lottery, there are n people who participate. My odds of > winning must be .5, either I do win or I don't. However, what if there > is only one person who participates in the lottery, and that person is > me? Isn't my odds of not winning 0, since I would always win? > > However in a system where probability is always calculated by the > desired events divided by the total number of possible outcomes, this > contradiction is explained, and empirically valid with your perceived > paradox with conventional frequency based probability. Given one desired > outcome (rolling a 1) and two potential outcomes (rolling or not rolling > a 1) the expression becomes 1 in 2. Charles' example though derives from > rolling a 1 as opposed to rolling a 1,2,3,4,5,6. With the same equation > structure of desired out of total outcomes, you get 1/6. Here is where > your interpretation breaks down though: what is the probability of > rolling a red? Your view would have either red, or not rolling a red, > thus 50-50. However, you can never roll a red. So the probability is > accurately reflected as 1/0.
But it ultimately makes as much sense to my intuition as this: > iQIcBAEBCgAGBQJQi58mAAoJEDeph/0fVJWsN84P/0GaRnK0CH8SR7IQsWoQcsx8 > 4t9kaO59i7l/vgw9PVc4AU7Vkoixj0Q3W/jiw7IYIgejCVWdzvPWJynUhd/U+gDF > 3nMK+iTNOOUjZjEZRv8e6Oki/io2AHfRZRjP/ugNOkOspdo+H78r1fmXOs5yXlqh > i++NP2DAXJ3k+BTc7043PrLvdIOtlrryGNPXG4qs8tvkvtC3v/Wjqq0k0d34RE3T > O5AnymocsoBDm9pYAOuxRveXcphMb1zA0zE3zBQmHW9JDfvNqad5o+/QbLjjpwQw > NWjLkR7PIOA/CUv9XTyVQwLw9LjHr1m+y68ZNMdsgQR4VF1CK0F4qL7QPKLJEIJs > 4GPGlPqg1XUK54PkQqQDSQYSj/rosQqBVUVUxlQPALxIHpfxLWqtG3T67j2Rk8Oo > qObTNoBksJTYu81Ii1VX3Pvt4bjogZgUcH6HJBPc0aIxOnHK4LGQ6p55xuSKLMSy > vfcf6NyGiyoQcziUHMGVdMjdKoy9PPGvRLsov3ezNxvePw/cunMwVnJacBZgf6+/ > mU9FLmTpeH18phe+QorheMwA/M9nnS13C/48fGoRFqKt19x+fVOVrtUiubgkAlS7 > sx8J9WL8FbT0D5HmrRB6DRavYxQIO4PCsGODBqag22GYBp6vR6GU8/dJe4hz95Yi > PbIz9P4Wml4NillJLvwk
