probability (eating birds)
hello,I'm studying for an exam,and I need some help with this one:
assume that the time units are discrete:
there are 3 birds A B & C,at each time unit a bird can eat or guard,with probability 1/2 independently from the other birds,or her previous action.
at each time unit a hawk arrives,and if there is not 1 guard at least ,he randomly eats one of the birds.
a)if X is a random variable which counts the time it took for the hawk to eat all the 3 birds then E(X)=?
b)if the hawk didn't eat bird A first then her expected life span is?
help would be appreciated..thanks