In CS, there's a systematic way to check if your code is buggy or not as you write code. Is there a way to check the correctness of your answer to a probability question without using a textbook?
For example, my friend proposed a solution to a probability question that seemed right.
Question: Suppose that each of N men at a party throws his hat into the center of the room. The hats are first mixed up, and then each man randomly selects a hat. What is the probability that none of the men selects his own hat?
Proposed Solution: if we suppose there are 8 men, then the suggestionw as (7 / 8) * (6 / 7) * (5 /6 )... * (1/2) * 1
which for the n case simplifies to 1/n
The argument sounded reasonable, but the answer was wrong which I found out from the textbook. I had to think about it a bit before I realized he had undercounted. Is there a more systematic way to check answers for probability questions?