Question

What is the conditional probability that exactly four heads appear when a fair coin is flipped five times given that the first flip came up tail?

Answer 1

Presumably, the coin tosses are independent of one another, so

$P(\text{exactly 4 heads}\mid\text{first flip is tails})=P(\text{exactly 4 heads})=\dfrac1{2^4}=\dfrac1{16}$

But if the coin flips are not independent, then we can't really say anything about this probability without any more information about how the flips are related...