"Prob(11th flip is a tail AND 10 heads in a row)" basically means that... suppose H= Heads and T=Tails. Then the event you are looking for is HHHHHHHHHHT.
You can use the geometric distribution formula: P(X=k) = p*(1-p)^k where p is the probability of success and there are k failures before your first success. So P(X=10)=0.5*(1-0.5)^10=0.5^11 is your answer to Prob(11th flip is a tail AND 10 heads in a row). So divide the answer by the answer you obtained in the first question to get your final answer.
Even without doing any computation, intuitively one can see the answer is 50% because the question is basically asking "Given that you got 10 heads in a row, what is the probability your 11th trial will result in a tail." Since coin flipping is independent, it doesn't matter what your previous results were.