A mathematician is
performing a probability experiment.
Starting from 0 (zero) on the integer number line, the mathematician
flips a coin and takes one step to the right if it comes up a head or one step
to the left if a tail. This process of flipping and moving either right or left
is repeated for a given number of flips of the coin.

This project computes the

*probability*of ending the walk at position*p*after*f*flips of the coin.
Here is a screenshot reporting
the probability of ending a random walk at +3 after 5 flips as 5/32 instead of
its decimal equivalent 0.15625.

Note that the screen shows
the positions that can be reached for a given number of flips as red-rimmed
black circles. Those that cannot be reached as a function of the number of
flips are represented as white circles.

The number of possible paths to each possible position for a given
number of flips is shown as a number above each possible position. It’s an
interesting fact that these numbers are given by Pascal’s triangle and the nCr
notation for *combinations*computes these numbers. The screen also shows that the totals number of possible paths for a given number of flips is a power of 2.

The probability for ending a
walk at position

*p*after*f*flips is the number of paths to position*p*divided by the total number of paths for the given number of flips.
This is the link to this
project,

*Random Walk on the Integer Number Line Probabilities*.
A detailed explanation of
the mathematics and the programming used in the project, including a couple of
additional programming simplifications, are detailed in document that is available at no cost
by sending an email request to grandadscience.com.

This Scratch project needed
a power of 2 script, a factorial script, and a nCr script that are available as
separate Scratch projects by clicking on the links as shown below.

**Combinations**

**Factorial**

**Powers of 2 Calculator**

These are the links to my other

*Random Walk on the Integer Number Line*projects.**Feynman’s Random Walk**

**Random Walk with Barriers**