If an apple has 3 flies land on it what is the probability that all three are on points in the same hemisphere?

Answer 1

this is a poorly posed question. is the apple on a table or hanging from a string? do flies land independently on apples? do they like to avoid each other or the string? do they like to mate? do they land on the side that's most visible or tasty? is the apple a perfect sphere, for example, where "half" has real meaning? these questions have to do with "independence", etc. "do the flies land at random on the apple, so each landing's an independent trial?" is a good question to ask. what is the meaning of "same side"? as in, how is a "side" (or half, or hemisphere) defined? if flies don't land at the same time, is the first "side" to be landed on the "side" under consideration? or is this about each of the three randomly landing on a particular ly prespecified half of the apple? in that case, it could be 1/2*1/2*1/2=1/8 (1/2 chance for each fly, like 3 "heads" coming up with 3 coin flips). if it's defined as the "side" where the first fly lands, it's a matter of how that side is defined. but you might say that the other two, landing at random (unlikely for a fly!), might go 1/2*1/2=1/4 (each of the other two flies landing at random on the "side" set out by the first - 50/50). regardless, the question obviously has to be much more precisely asked than this to be answered.