# 3.12 Probability topics: probability lab (edited: teegarden)

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This module presents students with a lab exercise allowing them to apply their understanding of Probability. Using a Minitab simulation, students will compare theoretical probabilities with experimental probabilities as it relates to dice. They will also investigate the effect of sample size.

Probability Lab

## I. student learning outcomes:

• The student will calculate theoretical and empirical probabilities.

• The student will appraise the differences between the two types of probabilities.

• The student will demonstrate an understanding of long-term probabilities.

## Ii. theoretical probability for the sum of two dice

Begin by looking at Theoretical probabilities for the sum of two dice. Let the value in the first row be the result for Die 1 and the value in the first column be the value for Die 2. Input the sum of the corresponding row and column in each box.

 + 1 2 3 4 5 6 1 2 3 4 5 6

## Using the following table, record the theoretical probabilities.

 Sum 2 3 4 5 6 7 8 9 10 11 12 Count Probability

Using the table above, determine the following theoretical probabilities

1. P(sum less than 5) = _________________

2. P(sum at least 9) = _________________

3. P(sum at most 6) = _________________

4. P(sum more than 7) = _________________

5. P(sum between 3 and 8) = _________________

6. P(sum less than 11) = _________________

## Iii. experimental (empirical) probability for the sum of two dice

Rolling the dice Using Minitab, simulate rolling two dice 360 times and finding the sum. Use Calc → Random Data → Integer, 360 rows and save in die 1, die 2.

Then use the Calc → Row Statistics. Select Sum, the two die columns and save in Sum Use Stat → Tables → Tally to summarize the data.

## Record the experimental probabilities:

 Sum 2 3 4 5 6 7 8 9 10 11 12 Count Probability

Using the table above, determine the following experimental probabilities

1. P(sum less than 5) = _________________

2. P(sum at least 9) = _________________

3. P(sum at most 6) = _________________

4. P(sum more than 7) = _________________

5. P(sum between 3 and 8) = _________________

6. P(sum less than 11) = _________________

## Iv. essay questions (on a separate sheet of paper, answer these questions in complete sentences.)

1. How do the empirical probabilities compare to the theoretical probabilities? (You may wish to convert the probabilities to percentages for ease of comparison.)

2. If you increased the number of times you rolled the dice to 720, would the empirical probability values change? Why?

Rerun the simulation and record your results.

 Sum 2 3 4 5 6 7 8 9 10 11 12 Count Probability

3. Did the increase in the number of trials cause the empirical probabilities and theoretical probabilities to be closer together or farther apart? Why? (You may wish to convert the probabilities to percentages for ease of comparison.)

ATTACH THE SESSION WINDOW WITH YOUR RESULTS AND THE ESSAY ANSWERS TO THIS COVER SHEET.

are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
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