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Probabilistic Number Theory Project Description Prerequisites Warm up Problems Hints Resources Teaching Notes Extension Problems Results

Warm Ups for the
Probabilistic Number Theory Problem

What is the probability that a positive integer chosen at random

  • is even?
  • is odd?
  • is divisible by 3?
  • leaves a remainder of 1 if you divide it by 3?
  • is divisible by both 3 and 5?
  • is divisible by both 2 and 6?
  • is not divisible by 3?
  • is divisible by neither 3 nor 5?

Explain your answers.

Another problem:

Find a way to generate a string of 1000 consecutive numbers, none of which are prime.

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