Probability of Meeting Again in a Random Walk

In summary, the question asks for the probability of two men, starting at the origin with a 1/2 chance of moving left or right, meeting again after N steps. It may be helpful to consider their relative position. The probability for one person is given by Wn(n1) = N!/[(n1!)(N-n1)!]*p^n1*q^(N-n1), where N is the total number of steps, n1 is the number of steps to the right, and p=q=1/2. However, it is unclear how to combine or adjust this for two people. It is also possible that an integral from 0 to N steps may be involved in the solution.
  • #1
mathlete
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The question:

"Two men start out together at the origin, each having a 1/2 chance of making a step to the left or right along the x-axis. Find the probability that they meet again after N steps."

It then says it may help to consider their relative position but I don't see how that would help.

The probability for one person is Wn(n1) = N!/[(n1!)(N-n1)!]*p^n1*q^(N-n1)

where N is total steps, n1 is steps to the right, p = q = 1/2 (for this problem). I just don't know how to combine/adjust it for two people.

Also, I'm not sure, but would this involve an integral from 0 to N steps at some point (to cover all cases)?
 
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  • #2
i commented on the other post... hopfully it can help you
 

FAQ: Probability of Meeting Again in a Random Walk

What is probability?

Probability is the measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

What is the difference between theoretical and experimental probability?

Theoretical probability is the probability of an event occurring based on mathematical calculations, while experimental probability is the probability of an event occurring based on actual experiments or observations.

What is a random walk?

A random walk is a mathematical model that describes the path of a randomly moving object, where each step is determined by a random variable. It is often used to analyze the behavior of complex systems.

What is the law of large numbers?

The law of large numbers states that as the number of trials or observations increases, the experimental probability of an event will approach its theoretical probability. In other words, the more data we have, the more accurate our predictions will be.

What is the central limit theorem?

The central limit theorem states that when independent random variables are added, their sum tends to follow a normal distribution, regardless of the distribution of the individual variables. This makes it a useful tool for analyzing and predicting outcomes in various fields, such as finance and statistics.

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