There is a box in which distinct numbered balls have been kept. You have to pick two balls randomly from the lot.

If someone is offering you a 2 to 1 odds that the numbers will be relatively prime, for example

If the balls you picked had the numbers 6 and 13, you lose $1.

If the balls you picked had the numbers 5 and 25, you win $2.

Will you accept that bet?

Yes, you should accept the bet. Simply because the odds of picking two relatively prime numbers are 60%. It is a win-win situation for you if you keep playing.