1. Calculating Probabilities for Chance Experiments with Equally Likely Outcomes

2. In this bag There are yellow, green, red, and blue pieces of paper. I am going to take 20 pieces out, one at a time, without replacing them. Record the results in the table provided

3. Before We Begin What does it mean to pull the pieces of paper out randomly? What does it mean to draw without replacing?

6. There Were 40 Pieces in the Bag When We Started If there were 40 cubes in the bag, how many cubes of each color were in the bag? Explain. If your teacher were to randomly draw another 20 cubes one at a time and with replacement from the bag, would you see exactly the same results? Explain.

7. Results The bag contains 10 of each color. Did your results reflect this? Explain.

8. Theoretical Probability vs. Experimental Probability Theoretical – What you think should happen. Your “theory” or educated guess based on evidence Experimental – What actually happened when the experiment was done. Calculation based on actual results

9. Theoretically

10. Experimentally However, chances are that in the experiment, the experimental probability was not the same. It is possible that after drawing 20 colors, that not one of them was red. Based on these results, we might assume that there are no red papers in the bag at all. This is based on the results of our experiment.

11. Flipping Coins We will be flipping a nickel and a dime at the same time What is the sample space of flipping a coin? What are the outcomes?

12. List all the possible outcomes NickelDime What is the theoretical probability of getting heads on both the nickel and the dime? What is the theoretical probability of getting exactly one heads?

14. Consider an experiment of randomly selecting a letter from the word number. – What is the sample space? List the probability of each outcome in the sample space. – What is the probability of selecting a vowel? – What is the probability of selecting the letter z?

18. Closing An experiment consists of randomly drawing a cube from a bag containing three red and two blue cubes. 1. What is the sample space of this experiment? 2. List the probability of each outcome in the sample space. 3. Is the probability of selecting a red cube equal to the probability of selecting a blue cube? Explain.