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.
An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?