Probability - Thank you for answering

Question

thank you very much for the help!

Answer 1

This problem is not a math/stats problem so much as it is a problem about independence.

Let's think about this in real terms: every odd intersection (1,3,5,...), we will be making a decision to go left or right. In those situations, we won't be driving North at all-- we'll be driving east or west! Think about it on a grid. We know we start driving North, and, at intersection 1, we'll go left or right. Then we'll go North or South, but then we're back to going left or right at intersection 3. Thus, the probability that we'll be going North (or South, for that matter), at any odd intersection is 0. There's no way we can go.

But, at even intersections, we're bound to go either North or South, since we're on a grid. We're told that we randomly turn up or down. Does what I did at intersection 2, then, make a difference at what I do at intersection 8? Not at all. Thus, the probability that we turn North at any even intersection is .5.

This is a key question about independence -- the actions we have taken in the past does not affect the actions that we take in the future.