- #1
Loren Booda
- 3,125
- 4
Starting out at zero on a number line and moving in succession one unit right or left at random, what is the probability that you will eventually return to zero?
CRGreathouse said:If the probability of moving left is different, the probability drops below 1.
Borek said:More seriously, if we are allowed to walk for ever probability of visiting any point approaches 1.
CRGreathouse said:I don't think so. If you move left with 60% probability, I calculate the probability of return as between 71.57% and 71.58%. (Once you start going left, you risk never coming back.) You have a finite expected maximum excursion to the right in that case.
kenewbie said:Any ideas on how to compute the chance of an outcome in an infinite series of weighted coin-tosses?
ie, if my coin has a probability of .7 to land heads, what is the propability of an infinite string of tosses that are all heads?
Borek said:What is probability of H? HH? HHH?
CRGreathouse said:If the probability of landing heads is less than 1, the probability of an infinite string of heads is 0.
kenewbie said:There must be some chance, however small?
kenewbie said:Rationally I see that it will hit zero if I try it, but if one imagine an infinite amount of infinite strings, then I can't see that there isn't room for one in which all are heads. In fact, there should be room for an infinite amount of all-heads strings.
A random walk is a mathematical concept that describes a path made up of a series of random steps. It is often used to model the movement of particles or objects in a random environment.
The origin in a random walk refers to the starting point of the walk, usually represented as the coordinates (0,0) on a graph.
A random walk "returns to origin" when it ends up back at the starting point after a series of random steps. This can happen multiple times during a walk, depending on the number of steps taken.
The chance of a random walk returning to origin depends on the number of steps taken and the type of random walk being performed. For a simple random walk, the chance of returning to origin is 1 divided by the square root of the number of steps. For more complex random walks, the chance may vary.
The chance of a random walk returning to origin can be calculated using mathematical equations that take into account the number of steps, the type of random walk, and other factors such as probabilities of different step sizes. These equations can be complex and may vary depending on the specific scenario.