Gold Digger Airlines run a daily shuttle between San Remo and Dry Creek. They have two aircraft: a two-engine DC-3 that used to belong to a Columbian drug cartel, and an old four-engine DC-6B bought from the US Army. All the six engines, that is, all the engines on both planes, have the same probability p of failing. For both planes: find the probability that half the engines will fail

(a) when p = 0.001;

(b) for p in general;

(c) let’s assume you hold your life dear, and that a plane will crash if half or more of the engines fail. For which values of p should you prefer the two-engine DC-3 (given that you fly at all)?