I hope the title accurately reflects my question.
I have an independent event, with a 98% chance of occurring.
Now, I observe and record the outcome of this event 100 times.
What is the probability that there is a single run of 17 consecutive occurrences?
Put another way that I don't think changes the question, given an unfair coin with a 98% chance of landing on heads, after a hundred flips, what is the probability that the coin landed on heads 17 consecutive times?
Per whuber's questions, use the following clarifications:
The desired probability is a trial with a run of at least 17 heads. Furthermore, the desired probability is a trial with at least one such run