Puzzle of the Week #31 - Engine Failure

This is an excerpt from my first book, Very Clever Puzzle Compendium: http://www.lulu.com/spotlight/maxelkat

Orville and Wilbur are model aeroplane enthusiasts.

Orville: These new engines you bought are terrible – they keep breaking down in mid air.

Wilbur: I know! That’s why I’ve fitted my new plane with two engines, and as long as at least one of them is still working, it will continue to fly.

Orville: I’ve gone even better: I’ve fitted mine with four engines, and as long as at least two of them are still working, my plane will stay up.

Wilbur: That’s not necessarily better – it depends on exactly what the probability is of each of the engines failing.

Orville: How do you mean?

Wilbur: Well, for instance, if the individual engines break a quarter of the time, the chance of your plane falling from the sky just over five percent, and mine would fail just over six percent of the time.

Orville: So mine would be better!

Wilbur: Yes, but what if the engines break down exactly half of the time? My plane would come down a quarter of the time, and yours would crash just over thirty-one percent of the time – so mine would be better!

As it turned out the probability of each of the engines malfunctioning was a magic figure somewhere between one quarter and one half, where the probability of Wilbur’s two-engine plane and the probability of Orville’s four-engine plane crashing was exactly identical.

What was the probability of each engine failing?