Each individual in a certain group of people rolls a fair ten sided dice an infinite number of times in order to generate a real number between 0 and 1. Using this method one individual generates the number 1/3. How many people must this group have in order for it to be likely that at least one of them would generate the number 1/3 using the above mentioned method of generating random real numbers between 0 and 1?
Idk what's on the dice?
Each dice has the numbers 0 through 9 on it.
So if you roll 3 and 9 does that generate 1/3?
No: the first roll generates the first digit, the second one - the second digit and so on. For example, rolling 7 and then 4 makes your number starting from 0,74... And, of course, no finite number of people in our group is enough. Even if we have one person for every rational number, it is still hopelessly far from enough.
Well, it might seem like it would only take one individual, but I suspect a trick question, because clearly, one is not a "group". The answer is probably that it would take an infinite number of people. Because they roll an infinite number of times, and (if?) we can only consider the last number in the sequence of rolls as the one that counts as being legitimately generated (a "real number" (singular) not "real numbers" (plural))... then with an infinite number of people rolling the dice, at any given moment there is always a 100% chance that the target number has been rolled, and so "lasting", and thereby possibly worthy of being actually counted and considered as a genuine generation.
why can't you just say everyone gets assigned a random real number. just seems like you are trying to make it as difficult as possible to read
You don't really seem to understand the question. Every person in our group rolls a dice infinite number of times, but thus generates just one real number, as I described above. And - as I already mentioned - infinitely many people may be not enough. There is, let us say, more than one infinity... (EDIT: I responded to Xochinla; P-wnattack, I think that Acgusta2's description is a nice way to imagine choosing a random real number.)
Without some formula (for instance using division), there is no way to generate a fraction number from a sequence of whole numbers. I assume the assignment of the digits on the dice to fractional values, or the usage of some formula because of the assertion that one did indeed generate the number 1/3 from rolling a "ten sided dice". Unless of course a pair of dice is used, perhaps of different colors, assigning one digit to the numerator and the other the denominator.
The formula is easy. Let us have an infinite sequence s1, s2, s3, ... of "whole" numbers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; let g be the real number we want to generate. Now we take g=(s1*10^-1)+(s2*10^-2)+(s3*10^-3)+... Actually, it is pretty basic and it was described above in a bit less formal way.
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