OzoDices

By G. Piani

Adapted from M. Bubani “Lanciamo i dadi con OZOBOT” [1]

In this activity we aim at studying the probability of exiting a number (or couple of numbers) by throwing one or two dices

Material:

OZOBOT; Cards with different Paths; Counting tables

Procedure:

• STEP 1 – Becoming acquainted with Ozodice

In the first step, we’ll become acquainted with the aleatory behavior of an uncoded Ozobot.

Take the Card #1. Put OZOBOT on a starting point and let it randomly move. Take note of the arrival number on the counting table.

Repeat the measure at least 50 times.

Calculate the absolute and relative frequency for each event.

Graph the result by an histogram (absolute frequency) and a pie chart (relative frequency).

• STEP 2 – Classical vs. Frequentist Probability

In this step, we’ll verify the convergence of frequentist probability to classical one.

Repeat Step 1 procedure using Cards #2 and #3 and #4, calculating a priori the probability of each event by means of classical probability theory.

Warning: in case of asymmetric path (like in case of Card #4), take care in using always the same starting point.

Are the results equal in the three cases?

Have your classical predictions been fulfilled?

• STEP 3 – Combining events

In this step, we’ll approach the probability of composite events.

Using two OZOBOTs from the two starting points (or merging two different OZOBOT run), measure the occurrence of couple of numbers (a,b), following Step 1 strategy.

Calculate the absolute and relative frequency for each composite event.

Graph the result by an histogram (absolute frequency) and a pie chart (relative frequency).

Does the result change if you take into account the order of the numbers in the couple (dice1, dice2)?

Are you able to predict your result by means of classical theory?

What do you expect from Card #5? Repeat the experiment in order to verify your prediction.

Can you draw new path in order to obtain a previously decided probability distribution?