How to make clear tasks for students about resolving paradoxes?
Let your students debunk a wrong argument

Present a specific faulty argument based on intuition. Then let your students find the flaw in it. This way you relieve your students from the burden to divine what you consider intuitive. They also have a more specific task that cannot be solved by just deriving the correct result.

For example a task for the birthday paradox could be:


  Bob argues:
  
  
    A random person has a different birthday from me with a probability of 364/365 (ignoring leap years, seasonal variations, etc.). Hence, if I am in a group with n−1 other people, the probability that all of them have a different birthday is (364/365)n−1. This probability is first smaller than 0.5 for n = 254.
  
  
  Find the flaw in Bob’s argument.