Hypothesis Tests · Superchallenge problem

Two researchers each see the same 12 coin tosses: 9 heads and 3 tails, the last toss a tail. Researcher A had planned exactly 12 tosses; Researcher B had planned to toss until the 3rd tail appeared. Both test $H_0\!: p = \tfrac12$ against $H_a\!: p > \tfrac12$ ($p$ = probability of heads), using the probability of a result at least as extreme under their own plan. Find Researcher B's exact p-value. Give a fraction.