Twelve Days of Christmas: Theoretical Probability

Twelve Days of Christmas

Today we began discussing probability (the likelihood an event will happen).  I explained that we are going to put all 364 gifts into a jar (in the form of pony beads) with each gift being assigned a color.  Our question today was, "What is the probability we would pull --- from the jar?"

To determine the probability we worked through THEORETICAL probability.  

Theoretical probability is what SHOULD HAPPEN.  

We completed the following spreadsheet to find the theoretical probability of each gift:

First, we look at the fact that "my true love" was given 12 partridges in a pear tree out of a total of 364 gifts.  We have the fraction 

12/364

Second, we turn this fraction into a decimal.  To do this we use division.  I had to discuss with my classes that a small number CAN be divided by a larger number.  When we divide a smaller number by a larger number we get a decimal (we used calculators)

12 ÷ 364 = 0.032967

We do not use the entire decimal number, we just want the number to the hundredth's place. 

0.03

Third, we turn this decimal into a percentage.  Basically, percent means "out of 100".  Since we have our decimal to the 100ths place, we drop the decimal point and we have our percent:

3%

This percentage tells us how many times we SHOULD pull a black bead from the container tomorrow.  We SHOULD pull a black bead 3 times from the container because we will be pulling a bead (and returning it) 100 times.

We did this for each gift he gave her.  Our completed spreadsheet looked like:

Finally, we turned all of our percentage data into a circle graph.  This will allow us to visually see the patterns that developed in our data.

HOMEWORK:

1. Complete the bar graph
2. Countdown 2.2