(:title Dice Difference Problem: 6th grade probability :)
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[ valign=middle]%c12 exa%*** Click on
[]Attach:Activity/cat1try.jpg Attach:Activity/down_cat.gif
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To use offline, download and unzip [[http://mathcasts.org/mtwiki/uploads/Activity/DiceDifference.zip|%exa%DiceDifference.zip%%]].
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Scratch file designed by [[mailto:emath@emathforall.com?subject=scratch|Linda Fahlberg-Stojanovska]].
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%c12 mor b%Activity Notes%%
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We throw 2 dice - %ref%1 Blue%% and %pra%1 Green%%.
%c11 exa%What is the difference in values?%%
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>>&<<%exa%The difference can be 0, 1, 2, 3, 4, '''or''' 5%%
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%pra c11%I say to my friend:
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%reg c11%I win if the difference is a 0, 1 or 2.
%up c11%You win if it is a 3, 4 or 5.%%
%ref c11%Each of us has 3 chances to win.%%
%exa c11%Let's play!%%
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(:showhide init=hide div=div1 lshow="+" lhide="-":) %c11 exa%Guided Activity%%
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%c11 bgr%Do the experiment 200-1000 times.%%
* Is my game fair?
* Which difference happens most often?
* Which difference happens least often?
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%sol%Now for some dreaded theory ...%%
*Make a table with the %pra c11%value of the green die%% across the %pra c11%top row%% and the %ref c11%value of the blue die%% going down the %ref c11%first column%% and the difference between the values at their "intersection" (:showhide init=hide div=div12 lshow="+" lhide="-":) Show me!
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-> Attach:die_game.jpg
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*Theoretically, how many possible combinations of dice can be thrown?
*Theoretically, how many of these combinations will have a difference of 1?
** How many ways can a difference of 5 happen?
** What percentage of times should 0 happen?
*Does this agree with your experimental results?
*What is the percentage of times that a 0, 1 or 2 occurs? How about a 3, 4 or 5?
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%sol%The 6 events - a difference of 0, 1, 2, 3, 4 or 5 are mutually exclusive and complete. "Mutually exclusive" means no 2 events can happen at same time and "complete" means no other events can occur.%%
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%rel b%Related Topics%%
* [[2Balls|2 Balls - Vertical Box]] %sol s9%6th grade probability%%
* [[4Balls2Boxes|4 Balls - 2 Reds and 2 Greens Drop into 2 Boxes]] %sol s9%8th grade probability%%
* [[6Balls3Boxes|6 Balls - 3 Reds and 3 Greens Drop into 3 Boxes]] %sol s9%8-10th grade probability%%
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