To find out how long it would take to meet a blue-haired person, we can calculate the expected number of people you need to meet on average before encountering one with blue hair.

The probability of meeting a blue-haired person in one encounter is $0.000000968$. Therefore, the probability of not meeting a blue-haired person in one encounter is $1 - 0.000000968$.

Now, to find the expected number of encounters (\(N\)) until you meet a blue-haired person, you can use the geometric distribution formula:
$$E(N) = \frac{1}{p}$$

Where:
- $E(N)$ is the expected number of encounters.
- $p$ is the probability of success in one encounter.

In this case:
$$E(N) = \frac{1}{0.000000968} \approx 1,033,058.$$

So, on average, you would need to meet approximately $1,032,648$ people before encountering one with blue hair.

If you meet $3$ people every day, you can calculate the time it would take by dividing the expected number of encounters by the number of people you meet each day:
$$ \text{Time (in days)} = \frac{E(N)}{\text{Encounters per day}} $$

$$ \text{Time (in days)} = \frac{1,032,648}{3} \approx 344,352. 67 \text{ days}$$

It would take approximately $344,352.67$ days, or about $943.43$ years, to meet a blue-haired person if you meet 3 people every day.