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(:title Ball Mixing Activity: 6 Balls in 3 Boxes - 8-10th grade probability:) [table border=1 cellpadding=5 width=100%] [row] [c] [table border=0] [row] [ valign=middle]%c12 exa%*** Click on  []Attach:Activity/cat1try.jpg  Attach:Activity/down_cat.gif [ valign=middle]%c12 exa% to see the whole action ***%% [tableend] ---- (:html:) (:htmlend:) >>&<< 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?%%]] >>&<< Scratch file designed by [[mailto:emath@emathforall.com?subject=scratch|Linda Fahlberg-Stojanovska]]. [ valign=middle] (:div222 style="margin-left:3px":) %c12 mor b%Activity Notes%% >>&<< ---- We have 6 balls - %red%3 Reds%% and %pra%3 Greens%%. We drop them randomly into 3 boxes. %c11 exa%What combinations are possible? >>&<< ---- >>&<< 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 >>&<< (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 ---- (:showhide init=show div=div1 lshow="+" lhide="-":) %c11 exa%Guided Activity%% (:div1 id=div1 :) >>&<< %c11 ans%Do the experiment 500-1000 times.%% * What is the percent of %bgr%mixed%%? * What is the percent of %yel%separate%%? >>-<< %sol%Now for some dreaded theory ...%% >>&<< %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? >>-<< %up%Suppose you drop%% %c11%two different colored balls into the first box%%. *What combination of balls remain? >>&<< -> 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? >>-<< *What are the theoretical probabilities of the two events:%bgr%mixed%% and %yel%separate%%? >>&<< %c12 exa%*Does your theory match your experiment?%% >>&<< (:div1end :) ---- (:div class="s9" style="margin-left:10px":) %sol%"Mutually exclusive" meaning both events cannot happen at same time and "complete" meaning no other event can occur.%% (:divend:) (:div222end:) [tableend] >>-<< * To change Scratch file, download and install freeware Scratch. See [[http://scratch.mit.edu|Scratch-MIT]] for more information. >>&<< ---- >>&<< %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%% >>&<< ---- >><< [table width=100% border=0] [row] [][[activity/| Attach:main/tri_purple_up_a.gif ]] [[activity/| Up one level]] [r](:html:) (:htmlend:) [tableend]