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A student who has just arrived to a class and takes some writing materials out of his pocket and places them on the desk. After a few minutes, he realizes that his pen (one that needs a cap) doesn't have it's cap on. He doesn't know if it came off when he took it out of his pocket or somewhere else. He carefully examines his pocket and then decides not to look for the cap. The cap was not in his pocket. Why did he not look anywhere else?

Maybe:

He noticed wet ink in his pocket. Wet ink means that while the pen was in his pocket, it had no cap and leaked. This was before he put the pen in his pocket, so at any point before he got to class.

Because

He found a death threat on a note from the thief in his pocket saying that him and his family would be murdered in their sleep if he ever tried to learn about the were about of his pen cap.

Or

He found a hole in his pocket which made him realize the pen cap could be anywhere.

Or

He realized that a 10 cent cap was not worth more than 10 seconds of his life.

Or probably simply that

His course was about to begin and had no time to do any thorough searches for a cap which was totally not necessary for the class anyway.

Maybe he realised

That is was a pop open pen that you click(they don't have caps).

OR

The cap of this specific pen was on another one of the writing materials.

Kind of an opposite to @Greg's answer.

He found no ink in his pocket and realized the pen had run out of ink