Estimating the range of $1$'s in an array of $0$'s and $1$'s

I have a large array $$A$$ that contains something like $$[0..1..0..]$$. It has a continuous range of $$0$$'s, followed by a range of $$1$$'s, and then another range of $$0$$'s.

This array is large and access is expensive, so I want to use a sampling algorithm to estimate the range $$(i, j)$$, where $$A_i$$ is the first $$1$$ and $$A_j$$ is the last $$1$$. Let's say I want to approximate this within an error of $$\epsilon n$$ where $$n$$ is the size of $$A$$, so that I get a range $$(i', j')$$ where $$|i' - i| \leq \epsilon n$$ and $$|j' - j| \leq \epsilon n$$.

What is an algorithm I can use to achieve this?