Data Projects
The theory of probability developed from a study of various games of chance by using coins, dice, and cards. Processes such as flipping a coin, rolling a die, or drawing a card from a deck are called probability experiments.
Based on your reading for this week:
Often when playing gambling games or collecting items in cereal boxes, one wonders how long will it be before one achieves success. For example, suppose there are 6 different types of toys with 1 toy packaged at random in a cereal box. If a person wanted a certain toy, about how many boxes would that person have to buy on average before obtaining that particular toy? Of course, there is the possibility that the particular toy would be in the first box opened or that the person might never obtain the particular toy. These are the extremes.
a. To find out, simulate the experiment using dice. Start rolling dice until a particular number, say 3, is obtained, and keep track of how many rolls are necessary. Repeat 100 times. Then find the average.
This is a lab experiment, just like you might find in any of the sciences. You are testing the statements in the text book that gives the probability of any one number coming up on a single thrown die. Make a chart – Tries vs Rolls (remember you have to keep rolling until your chosen number comes up…that is one try.). Keep track for 100 tries. (Share the load…get others to help have fun with you.) Then find the probability of your experiment with the text. Post your information and comment and remember to respond. (Hint: You will have somewhere between 575 and 750 rolls.)
Then answer these question about your results
a. What did this experiment have to do with this week’s reading?
b. What should we expect the average to be?
c. What accounts for the differences from what we would expect?
d. Would we get the same thing if we rolled another 100 experiments?
Reference: Course Text: Bluman, A.G. (2014). Elementary Statistics: A step-by-step approach (9th ed.). New York: McGraw-Hill.
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