100 socks
Here's a pretty easy question to solve in your spare time. Let's say you have 100 colored socks and four colored bags. The socks and bags are colored in various (and different) colors: You have to match socks and bags that's in the same color. (For example, matching a red sock with a red bag is a correct pair) What's the probability that you would manage to match only 99 pairs of socks and bags correctly?
Hint: The answer might be more simple than you thought.
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1 solution
Here's the oversimplified answer in case you want to check your answer fast: Since you matched 99 socks correctly, the other 1 pair has to be correct. So the answer is... [Drum Roll] 0%.
It's all pretty simple when you reduce the number of the socks. Let's say we have 3 socks and bags in red, blue and orange. If you match the blue bags with blue socks, and the red bags with red socks, there's no possibility of mismatching the rest. The result is same on a big scale, such as 150 socks or even 10,000 socks.
Conclusion: It's impossible to correctly match only N − 1 socks out of N socks in this kind of situations.