Question

A person is standing in the middle of a large plaza. The person randomly takes a step either north, south, east or west and then stops. From this new position, the person again randomly takes a step either north, south, east or west. If the person continues this for five steps, how far (straight line distance) would you expect the person to be from the original point after the five steps? Design and run a simulation. you may wish to place the starting position at the origin of the coordinate plane and use the Pythagorean Theorem to find the distance from the origin to the ending point. Remember to record the distance for each trial.
Thanks!

Answer 1

Answer:

distance between 2 and 3 away from the origin (0,0)

Step-by-step explanation:

I tried this as a simulation.

Let y = a random number.

for x := 1 to 1000 do begin

for y := 1 to 5 do begin

a := random(4)+1;

if a := 1 then v:= v +1           That is he's going north

if a:=  2 then v:=v - 1           That is south

if a:= 3 then h := h + 1         west

if a :=4 then h :h - 1             east

end;

end;

I am running a thousand simulations  

This not my actual coding. I'm made it so that it runs 5000 times

You don't have to keep score of the distance until the end.

Most of the time it gives me a distance of between 2 and 3. The quadrants are random The horizontal distance and vertical distance come in at 2 and 3 respectively or -2 and 3 or 2 and - 3 or -2 or -3 etc.

Setting this up as a tree would almost give you as many branches as a tree outside your window.  But you can try drawing it you like. At least one of them.

What are the chances of you going straight east on a run

Wouldn't it be 1/4 * 1/4 * 1/4 * 1/4 * 1/4 = 1/1024 = 0.000976

Now imagine the tree branch for this. There are over 1000 branches that it could take.

So five steps going east would be  -1 + -1 + -1 +-1 + - 1 = - 5 = h

Vertical = 0

Running this simulation occasionally does give 0.