1. Theoretical vs. Experimental Probability

2.  We are going to analyze the difference between theoretical and experimental probability  Definition for Theoretical and Experimental Probability:  http://www.onlinemathlearning.com/theoretical- probability.html http://www.onlinemathlearning.com/theoretical- probability.html

3.  List all the outcome for when you roll 2 number cubes. (Example: 1&1, 1&2, 2&1)Then record the following probabilities, in thery. Write these as fractions in simplest form. Then, change your fraction to a decimal. Now write your decimal as a percent (round to the nearest whole number).  1. P(sum of 2)_______________ 2. P(sum of 3)________________ 3. P(sum of 4)_______________ 4. P(sum of 5)________________ 5. P(sum of 6)_______________ 6. P (sum of 7)________________ 7. P(sum of 8)_______________ 8. P (sum of 9)________________ 9. P(sum of 10)______________ 10. P(sum of 11)_______________ 11. P(sum of 12)______________ 12. P(sum of 13)_______________ You have now completed Theoretical Probability for what can happen when you roll two number cubes.

4.  Now, let’s actually roll two number cubes and perform an experiment to see what we actually get. This is called EXPERIMENTAL PROBABILITY. Directions: Roll two numbers cubes 50 times. Put tally marks beside the sum of the number cubes after each roll.  For Dice visit: http://www.random.org/dice/ Sum Tally Marks 2___________________________________________ 3___________________________________________ 4___________________________________________ 5___________________________________________ 6___________________________________________ 7___________________________________________ 8___________________________________________ 9___________________________________________ 10__________________________________________ 11__________________________________________ 12__________________________________________http://www.random.org/dice/

5.  Form fractions showing how many out of 50 you have for each sum. Then, change these fractions into decimals and percents. Sum of 2 _____________________ Sum of 8_____________________ Sum of 3_____________________ Sum of 9_____________________ Sum of 4_____________________ Sum of 10____________________ Sum of 5_____________________ Sum of 11____________________ Sum of 6_____________________ Sum of 12____________________ Sum of 7_____________________ * For help with changing fractions into decimals, visit: http://www.webmath.com/fract2dec.html http://www.webmath.com/fract2dec.html

6.  COMPARING THEORETICAL AND EXPERIMENTAL PROBABILITY Let’s see how the different percentages compare. Fill in the data in the chart using your fractions, decimals, and percents. SumTheoretical Probability (What SHOULD have happened) Experimental Probability (What DID happen) 2 3 4 5 6 7 8 9 10 11 12

7.  Conclusion:  1. Did any of your theoretical probabilities match your experimental probabilities? If so, which sums?________________________________ 2. Which sums had higher theoretical probabilities than experimental? _____________________________________________________________ _____________________________________________________ 3. Which sums had higher experimental probabilities than theoretical? _____________________________________________________________ _____________________________________________________ 4. So, are theoretical probabilities always accurate? Explain. _____________________________________________________________ _____________________________________________________