A fair coin is tossed 14 times. Every string of heads and tails is equally likely…

Step 1. Exactly 7 heads. $^{14}C_7 = 3432$ strings, so $\dfrac{3432}{16\,384} \approx 0.2095$.

Step 2. At least 12 heads. $^{14}C_{12} + {}^{14}C_{13} + {}^{14}C_{14} = 91 + 14 + 1 = 106$. So $\dfrac{106}{16\,384} \approx 0.0065$.

Step 3. More heads than tails. By symmetry, more heads and more tails are equally likely. The two events together have probability $1 - 0.2095 = 0.7905$, so more heads has probability $\dfrac{0.7905}{2} \approx 0.3953$.