I get

3. 66.26%

Sometimes it is easier to find the complementary probability, i.e. the probability that you do not get 6 tails in a row. To that end, there are 2^100 possible sequences of heads or tails, each of which we assume are equally likely. Let be the number of sequences of n heads or tails in which there are not 6 tails in a row. It's easy to see that

for

and

For , consider the number of acceptable sequences ending in H, T, TT, TTT, TTTT, TTTTT. There are of these, respectively. So

for

We can use this recurrence to find that

(I used a spreadsheet)

so the probability that no sequence of 6 tails occurs in 100 flips is approximately

and the probability that at least one sequence of 6 tails occurs is