Given that we have already tossed a balance coin ten times a

Given that we have already tossed a balance coin ten times and obtained zero head. What is the probability that we must toss it at least two more times to obtain the first head?

Solution

We can forget about the 1st 10 tosses
there is a dictum, \"probability has no memory\"

since \"at least two more tosses \" is stipulated,
it could be ANY number of tosses beyond 11.
all that is certain is that the 1st toss should result in a tail
Thus reqd. probability = 1/2