A professor of mathematics suggests the following game to one of his student. We throw twenty times a coin. If no tail appears, the professor gives to the student one million$, but in the other cases the student pays 1 $ Would you play to this game?

You would play the game.

Step-by-step explanation:

The reason for this, is because although the chance to get no tails after 20 flips is very slim, there is very little repercussions for taking the bet.  You only have to pay $1 if you lose, but you get $20 million if you win.