Probability of crossing a point?

[moonman239]

Let's say there is a spider and an ant in a square box. The ant stays in the center of the box. The spider walks a random distance, in a random direction. What are the chances that he will meet the ant?

 

[SW VandeCarr]

If you're talking about two geometric points representing the spider and the ant, the probability is 0. If one or both are modeled to occupy a measurable space, the probability is 1 given a finite space and no time limit.

 

[honestrosewater]

The problem doesn't sound well-defined. How many possible directions are there for the spider to walk in? How many possible distances? (If you want to keep things simple, pick a finite number.) Where does the spider start? What is the shape of the path that the spider walks in? I can't agree with SW VandeCarr because, if the spider crawls in a straight line along the inside of the box, it's going to stay in one plane, and if the ant isn't in that plane, the spider can walk forever and never meet the ant.

 

[SW VandeCarr]

Let's say there is a spider and an ant in a square box. The ant stays in the center of the box. The spider walks a random distance, in a random direction. What are the chances that he will meet the ant?

The problem doesn't sound well-defined. How many possible directions are there for the spider to walk in? How many possible distances? (If you want to keep things simple, pick a finite number.) Where does the spider start? What is the shape of the path that the spider walks in? I can't agree with SW VandeCarr because, if the spider crawls in a straight line along the inside of the box, it's going to stay in one plane, and if the ant isn't in that plane, the spider can walk forever and never meet the ant.

I understood that by saying the spider walks in a random direction for a random distance, the OP was attempting to describe Brownian type motion in a finite space with no time limit. Otherwise the question makes no sense.

 

[blue_raver22]

The probability of the spider crossing a specific point in the box where the ant is located is dependent on a number of factors such as the size of the box, the distance the spider walks, and the direction in which it walks. Without more specific information, it is difficult to determine the exact probability of the spider meeting the ant. However, we can make some assumptions and estimations to provide a general idea of the likelihood of this event occurring.

Assuming that the box is a square with equal sides and the spider walks in a straight line in a random direction, the probability of the spider crossing a specific point in the box where the ant is located can be calculated using basic geometry. If the spider walks a random distance within the box, the probability of it crossing any given point within the box would be the same, assuming all points have equal probability of being crossed.

However, if the spider's movements are not completely random and it tends to walk in a certain direction or avoid certain areas of the box, the probability of it crossing the point where the ant is located would be affected. Additionally, the size of the box and the speed at which the spider walks would also impact the probability.

In summary, the probability of the spider crossing a specific point in the box where the ant is located is difficult to determine without more specific information. However, we can estimate that the probability would be influenced by the size of the box, the distance the spider walks, and its random movements within the box.