LogFAQs > #980323539

If the intended problem statement is this:

A plane has a 50% chance of crashing each time it flies. It is flown repeatedly until it crashes. Person X is a passenger on exactly one of these flights. The first flight has 1 passenger and the number of passengers doubles each time. What is their chance of dying?

Then we have a classic case of a vile math pun.

If "chance of dying" is taken to mean "conditional probability of dying on plane flight n, given that the plane has made n-1 trips", that is just 1/2. That's the risk any passenger takes when boarding that plane, no matter what has gone before.

If "chance of dying" is taken to mean "unconditional probability of being one of the dead in this fact pattern", then we get that series 1/2 + (1/4)(2/3) + (1/8)(4/7) etc.