Given that we have already tossed a balanced coin ten times and obtained zero heads, what is the probability that we must toss it at least two more times to obtain the first head

A balanced coin will have 50:50 chance of showing either head or tail. In this question, you are asked the probability to find the first head after two tosses. That means the toss result should be:
1. tail   = 1/2 probability
2. head = 1/2 probability

Previously you are tossing the coin 10 times and obtain zero head. But this previous 10 tosses result should not influence your probability in the 11th and 12th toss. The chance will always be 50:50 no matter how much the tosses count. So the probability should be: 1/2 * 1/2= 1/4

11/36 is .305 repeating