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Choose one of the outcomes listed above. Based on the sample space above, what is the theoretical probability that the outcome will occur? (write the probability as a fraction and as a decimal.)
Outcome:______TT3______ Probability: _____1/24 ; 0.0417______
EXPERIMENTAL (Empirical) PROBABILITY:
Using the same outcome you chose at the bottom of the previous page, conduct the experiment and record the number of times the outcome occurs.
Comment: This tells you to flip the coin one, then flip it again, then
roll a dice once. That would constitute one trial of the experiment.
Let's assume you perform the experiment 24 times.
You are to keep track of how many time tt3 occurs and record that
Outcome: put your number here______________
In the table below, “success” means that the above outcome occurred.
You will conduct the experiment a total of 100 times.
# of successes for each set of 10 trials
Cumulative number of successes
Proportion of successes based on all trials
Decimal estimate of successes based on all trials
Comment: Now you are perform the experiment 10 times and list the number of tt3.
Do it again for 10 trials.
Add up the number of successes as you go through each set of 10 trials.
First set of 10 trials /10
Second set of 10 trials /20
Third set of 10 trials /30
Fourth set of 10 trials /40
Fifth set of 10 trials /50
Sixth set of 10 trials /60
Seventh set of 10 trials /70
Eighth set of 10 trials /80
Ninth set of 10 trials /90
Tenth set of 10 trials /100
Look at the far right column of the table.
Comment: The far right column contains the cumulative sum of the decimal equivalents of the number of tt3's as you perform the trial more and more times.
How does the empirical probability compare to the theoretical probability as the total number of trials increases? What would happen to the numbers in the far right column if you repeated the experiment 1000 times?
Comment: As you increase the number of trials the emperical proportion of
tt3 results will get closer and closer to the theoretical proportion of
1 out of 24 = 0.0417