>TL;DR: How do you approach binomial probability when the sets are of infinite size?
For example, say you flip a fair coin an infinite number of times, representing every head with a "1" and every tail with a "0". The results will be of the form:
[00000000...00000000]
[00000000...00000001]
[00000000...00000011]
...
[11111111...11111100]
[11111111...11111110]
[11111111...11111111]
How would you calculate the probability that your resultant set will contain, let's say, exactly half heads and half tails. There are many sets for which this is true, such as:
[10101010...10101010]
[00110011...00110011]
[11111111...00000000]
And so on...
How do you calculate the probability that your coin flip experiment produces exactly half heads and exactly half tails? Is it probability zero? Or is this calculation impossible?
For example, say you flip a fair coin an infinite number of times, representing every head with a "1" and every tail with a "0". The results will be of the form:
[00000000...00000000]
[00000000...00000001]
[00000000...00000011]
...
[11111111...11111100]
[11111111...11111110]
[11111111...11111111]
How would you calculate the probability that your resultant set will contain, let's say, exactly half heads and half tails. There are many sets for which this is true, such as:
[10101010...10101010]
[00110011...00110011]
[11111111...00000000]
And so on...
How do you calculate the probability that your coin flip experiment produces exactly half heads and exactly half tails? Is it probability zero? Or is this calculation impossible?
