Three probability questions: 1) What is the expected number of digits of a number randomly selected from the set of all natural numbers? 2) If I pick two numbers, a and b, randomly from the natural numbers, what is the probability a > b? 3) Consider a particular number, say 1000. Now pick a single number x from the set of natural numbers. What is the probability x

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2024-08-01 20:27

Three probability questions: 1) What is the expected number of digits of a number randomly selected from the set of all natural numbers? 2) If I pick two numbers, a and b, randomly from the natural numbers, what is the probability a > b? 3) Consider a particular number, say 1000. Now pick a single number x from the set of natural numbers. What is the probability x < 1000?

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Douglas Ridgway
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4 小時內	Casey Bennetto casey.bennetto
11 小時內	Thomas Garrard thomasjhgarrard	I started out thinking surely it's inf:0.5:0. But then 2) just seems wrong, if you pick a number a from the infinite set, look at it, what is the probability that the next number is bigger. Essentially the answer to 3) can be applied to any number and will always be 0, so if you know what a is, b will always be bigger. This leads me to think you can't actually pick a number from the set...