Solutions
1. Pseudo's modified version of Homer's answer is correct. The actual answer is $2,000, but rounding errors kick it down to $1,955 and change. (you'll get a lot closer if you use the expected return of .674286129..., but $1955 is close enough).
2. Taking the sum of all of the probabilities, (1/10+1/10+1/55+1/400+1/400+1/89143+1/520000), you can confirm their approximation (the sum ~ .223, or 1/4.48). Since any $1 "winners" offer zero profit, you subtract 1/10 from this total probability to get approx 0.12319 (the probability of the ticket being profitable). Take the inverse, and you'll see that 1 out of every 8.12 tickets makes money.
3. Doh, the boss is watching... Gotta get back to work. Will post solution later.
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