Question

Suppose that a certain lottery pays out increasing amounts every week. Each week, a ticket can be purchased for $5. Assuming that the odds of winning are 1 in 200 million, there can only be a single winner, and you win the full sum of the prize, at what prize amount does the expectation become positive?

Answer 1

Let X be the price amount then we know the expectation is given by

This value is positive if

So price amount of 999,999,995, or more will make the expected value of price amount positive