A grid is an aid for the counting of routes and for the creation of binomial distributions
Routes
You can see how the routes are made from Start to each end point of the grid. Each route consists of a number of steps, some to the right and some upwards. All of the possible routes with a fixed number of steps generate Pascal’s triangle.
Binomial probabilities
The grid is a visual model for a binomial distribution. In the binomial model, the parameter p is called the probability of “success”, the parameter n is the number of “trials”, and the random variable X models the number of successes in n trials. In the case of the grid, a “success” is taking a step to the right, rather than up; the number of trials is the total number of steps taken in the grid to get from Start to an end point; and the number of success is the number of steps which were to the right.
Settings and buttons
The number of steps and the probabilities define the grid.
With the tempo bar you start the simulation and you see the routes created dynamically.
View
With Routes you will see the numbers of routes, just like Pascal’s triangle
With Routes table you see the details of the routes.
With Probability table the binomial distribution, with formulas, is shown.
With Bar chart the binomial distribution appears as graph.
Tempo bar
With the tempo bar you can change the speed of the simulation before and during the simulation.
With Step you can track the experiment step by step.
Fast is meant to create many data.
Interrupt/Continue
With the space bar you can interrupt or resume the simulation.
With the print button you obtain a complete preview, and you have the options to copy the complete tree to the clipboard, send it to Word, or print it immediately.