What's the probability of flipping an even number of heads after tossing 99 fair coins and one weighted coin. I don't know if this matters, but let's say the probability of the weighted coin landing heads is p.
Is the following correct:
P(even in 99 flips)*P(tails on last flip) + P(odd in 99 flips)P(heads in last flip) (1/2)[(99/100)(1/2) + (1/100)(1-p)] + (1/2)*[(1/2)(99/100) + (1/100)(p)]
This gets 1/2, but this doesn't logically make sense to me, because what is the last coin is p=0. Shouldn't it be less/more likely?