On a mailing list that I belong to, someone attempted to explain it to me (as also to children who are facing the concept for the first time). But....

I can TELL myself all this:

On Sat, Oct 27, 2012 at 2:15 PM, L H <ljrh....@gmail.com> 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/0

> 4t9kaO59i7l/vgw9PVc4AU7Vkoixj0Q3W/jiw7IY

> 3nMK+iTNOOUjZjEZRv8e6Oki/io2AHfRZRjP/ugN

> i++NP2DAXJ3k+BTc7043PrLvdIOtlrryGNPXG4qs

> O5AnymocsoBDm9pYAOuxRveXcphMb1zA0zE3zBQm

> NWjLkR7PIOA/CUv9XTyVQwLw9LjHr1m+y68ZNMds

> 4GPGlPqg1XUK54PkQqQDSQYSj/rosQqBVUVUxlQP

> qObTNoBksJTYu81Ii1VX3Pvt4bjogZgUcH6HJBPc

> vfcf6NyGiyoQcziUHMGVdMjdKoy9PPGvRLsov3ez

> mU9FLmTpeH18phe+QorheMwA/M9nnS13C/48fGoR

> sx8J9WL8FbT0D5HmrRB6DRavYxQIO4PCsGODBqag

> PbIz9P4Wml4NillJLvwk