And if your answer is that your utility for money is not linear
This is a very, very, very safe assumption when talking about $27 billion.
What would you do if you were in the least convenient possible world where your utility function for money is linear?
Then I would have radically different intuitions and responses to such tradeoffs and the answer would be obvious. This is like asking:
"Would you eat cow manure? No? Well what about in the least convenient possible world where eating cow manure is your sole and ultimate desire?"
What if the problem were phrased like this?
Set Four:
1.) Save 24000 lives, with certainty
2.) 0.0001% chance of saving 27 billion lives, 99.9999% chance of saving no lives.
Related to: The Allais Paradox, Zut Allais, Allais Malaise, and Pascal's Mugging
You've probably heard the Allais Paradox before, where you choose one of the two options from each set:
Set One:
Set Two:
The reason this is called a "paradox" is that most people choose 1 from set one and choose 2 from set two, despite set two being the same as a ~33% chance of being able to choose from set one.
U(Set One, Choice 2) = 0.97 * U($27000) = 26190
U(Set Two, Choice 2) = 0.33 * U($27000) = 8910
The Problem With "It is Perfectly Rational to Bet on Certainty"
The Problem With "People Are Silly"
When we go solely by the expected utility calculations we get:
U(Set Three, Choice 2) = 0.000001 * U($27000000000) = 27000
So here's the real dilemma: you have to pay $10000 to play the game. The expected utility calculations now say choice 1 yields $14000 and choice 2 yields $17000.
And if your answer is that your utility for money is not linear, check to see if that's your real rejection. What would you do if you would donate the money? What would you do if you were in the least convenient possible world where your utility function for money is linear?