Math 1.0 August 28: Two Dice Combinations and some Puzzles

Two dice combinations

Last week we had one dice, we figured out the possible outcomes, and then kids rolled dice, counted number of rolls for each case 1-6, and plotted them as histograms. 

This week we started by identifying possible outcomes of two die:

And then we counted the number of possible ways we could get each value between 1 and 12:

Left: possible outcomes of rolling two die
Middle: # of ways to get each outcome
Right: observed totals for class

So this week we saw that with two dice (unlike with one) we were more likely to roll numbers in the middle (7 is six times as likely as 2). The goal was not to begin computing probabilities though for those paying attention the probabiliity of rolling 7 (abbreviated p(7)) =1/6 and p(2) = 1/36.

  

While the students were busy rolling dice, Dr. Barishnikov found a website that simulated lots of dice. We looked at 1000 rolls of a single dice, and found the same as last week that there was an even probability of each outcome. Then we increased it to 2 dice. Below is what happens when we roll twenty dice (note: students thought rolling as many dice as many times as possible was very awesome).  

 Puzzles

Dr. Patel posed a puzzle: Who stole the diamond?