(a) The probability of obtaining two tails in one throw is \(\frac{1}{4}\). The probability of not obtaining two tails is \(\frac{3}{4}\). For the first time on the 7th throw, we need 6 failures followed by 1 success:

\(\left( \frac{3}{4} \right)^6 \times \frac{1}{4} = \frac{729}{16384} \approx 0.0445\)

(b) The probability that it takes more than 9 throws is the probability of failing 9 times:

\(\left( \frac{3}{4} \right)^9 = \frac{19683}{262144} \approx 0.0751\)