[IronUnkind]

A situation arises where X number of U.S. citizens will have a 75 percent chance of being instantly vaporized.

At the same time, your beloved child stands over a trap door in an undisclosed location which will open above one of THREE TUNNELS.

TUNNEL ONE leads to instant vaporization.
TUNNEL TWO leads to an excruciating death.
TUNNEL THREE delivers your child back to you unharmed.

You have a BIG RED BUTTON, which will save the US citizens from doom but will simultaneously open the trap door when you push it.

BUT...the BIG RED BUTTON fails to work 15 percent of the time.

What number does X have to be in order for you to choose to push the button?


Note 1: x must be less than infinite and greater than 0.

Note 2: You are a single parent of exactly one child.

Note 3: You own a private jet, and you and your son (if he lives) may fly to another unharmed part of the world in the event of the catastrophe.

Note 4: You are immortal.

Note 5: If the trap door doesn't open, your child is safe.