(:title Ball Mixing Activity: 6 Balls in 3 Boxes - 8-10th grade probability:)
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[ valign=middle]%c12 exa%*** Click on
[]Attach:Activity/cat1try.jpg Attach:Activity/down_cat.gif
[ valign=middle]%c12 exa% to see the whole action ***%%
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To use offline, download and unzip [[http://mathcasts.org/mtwiki/uploads/Activity/6balls_3R_3G_3Boxes.zip|6balls_3R_3G_3Boxes.zip]].
>>&<>&<<[[http://mathcasts.org/mc/scratch/how2offline/how2offline.htm|%ref%How do I do all this?%%]]
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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 have 6 balls - %red%3 Reds%% and %pra%3 Greens%%. We drop them randomly into 3 boxes.
%c11 exa%What combinations are possible?
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The following '''two events''' are mutually exclusive and complete.
(a) All 3 boxes will have %red%1R%%&%pra%1G%%.
We call this event: %c11 bgr%MIXED%% colors.
Attach:Activity/mix6box_mixed.png
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(b) box %pra%2G%%, box %red%2R%%, box %red%1R%%&%pra%1G%%.
We call this event: %c11 yel%SEPARATE%% colors.
Attach:Activity/mix6box_separate.png
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(:showhide init=show div=div1 lshow="+" lhide="-":) %c11 exa%Guided Activity%%
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%c11 ans%Do the experiment 500-1000 times.%%
* What is the percent of %bgr%mixed%%?
* What is the percent of %yel%separate%%?
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%sol%Now for some dreaded theory ...%%
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%bgr%Suppose you drop %c11%two same colored balls into the first box%%.
*What combination of balls remain?
*How many different ways can the remaining balls drop into the other boxes? %exa%What events occur?%%
*What are the chances that you will drop two same colored balls into the first box?
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%up%Suppose you drop%% %c11%two different colored balls into the first box%%.
*What combination of balls remain?
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-> Here: see %newwin%[[4Balls2Boxes|4 Balls - 2 Reds and 2 Greens Drop into 2 Boxes]]
*How many different ways can these remaining balls drop into the other boxes? %exa%What events occur?%%
*What are the chances that you will drop two different colored balls into the first box?
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*What are the theoretical probabilities of the two events:%bgr%mixed%% and %yel%separate%%?
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%c12 exa%*Does your theory match your experiment?%%
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%sol%"Mutually exclusive" meaning both events cannot happen at same time and "complete" meaning no other event can occur.%%
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* To change Scratch file, download and install freeware Scratch. See [[http://scratch.mit.edu|Scratch-MIT]] for more information.
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%rel b%Related Topics%%
* [[2Balls|2 Balls - 1 Red and 1 Green Drop into Vertical Box]] %sol s9%3rd grade probability%%
* [[DiceDifference|Throw two dice and check their difference]] %sol s9%6th grade probability%%
* [[4Balls2Boxes|4 Balls - 2 Reds and 2 Greens Drop into 2 Boxes]] %sol s9%8th grade probability%%
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