A coin, having probability p of coming up heads is successively flipped until at least one head and one tail have been flipped.
(a)Find the expected number of flips needed.
X=1, if the first flip results in heads
X=2, if the first flip results in tails
N: the total number of flips needed
At this point I'm obviously not able to solve for E[N] because they cancel each other out. What am I doing wrong? I've seriously been looking at this problem for four hours now.
There's another way that I just thought of doing the problem..
But I don't have the solution to the problem, so I can't be sure it's correct. Although I'm not very confident it is anyway..