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This is a test of link to a file and Equation Editor.

Waiting for a double


In this activity, students conduct their first simulation, collecting, displaying, and summarizing data to test a conjecture about probability. The activity draws upon their intuitive sense of probability and engages them in thinking more precisely about the topic. This is one of several activities in which intuitive notions about probability can be at odds with experimental or theoretical analyses.


When rolling two dice, what is the average number of rolls needed to roll a double? In this activity, students approach this question through collecting and analyzing data. By rolling two dice repeatedly, they collect many examples of how many rolls it can take to get a double.


Up to now, students have been exploring the unit problem informally. Now they begin a series of explorations designed to help them develop the tools they will need to answer the unit problem. The in-class portion of this activity has several parts: reviewing the homework, gathering class data, and graphing the class data.

Approximate time

5 minutes for introduction

20 minutes for activity (at home or in class)

25 minutes to collect and analyze class data

Classroom organization

Individuals, then small groups to review data, test Equation Editor: z 2 + 3 3 = 5 . 5 size 12{z rSup { size 8{2} } +3 rSup { size 8{3} } = sqrt {5 "." 5} } {} + 4. Then the whole class gathers to analyze data. This is a test of Equation Editor: z 2 + 3 3 = 5 . 5 size 12{z rSup { size 8{2} } +3 rSup { size 8{3} } = sqrt {5 "." 5} } {} + 4.

x 2 + y 2 = z 1 + z 2 size 12{x rSup { size 8{2} } +y rSup { size 8{2} } =z rSub { size 8{1} } +z rSub { size 8{2} } } {}

1 2 2 ³ AC ¯ BC ˆ i = 0 n alignl { stack { size 12{ { {1} over {2} } sqrt {2}³{overline { ital "AC"}} widehat widevec { ital "BC"} } {} # size 12{ Sum cSub { size 8{i=0} } {n} } {}} } {}

For a discussion of simulating class data, click here. For a Fathom file that can be used as a demonstration of the process followed during this activity, click here .

Key questions

Before assigning the activity:

How would you do this experiment?

Why is it important to get genuine data when doing activities like this?

How do you compute the average of a set of numbers?

During the class discussion:

How did you make your prediction?

What were the highest and lowest number of rolls you got?

How might you graph one student’s outcomes?

Can you visualize the average in terms of the graph?

How might we graph the outcomes of the entire class?

Is 1 a likely outcome?

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
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Source:  OpenStax, The game of pig. OpenStax CNX. Nov 19, 2007 Download for free at http://cnx.org/content/col10488/1.2
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