A spider eats 3 flies a day. Until the spider fills his quota a fly has a 50% chance of survival if he attempts to pass the web.

Assuming 5 flies have already made the attempt to pass, what is the probability that the 6th fly will survive the attempt?

Out of the 2^5=32 combinations of surviving flies among the first 5, in 5C3=10 have 3 been eaten, in 5C4=5 have 4 been eaten and in 5C5=1 have 5 been eaten. So the spider is satisfied 16/32 = 1/2 of the time and the new fly is safe.

Also in half the remaining cases (when the spider is not yet satiated), the fly also escapes, so he escapes 3/4 of the time, that is, with 3/4 probability.

Posted by Charlie on 2003-11-25 09:58:41