Statistics · Probability Topics
Probability Topics
CC BY 4.0 · OpenStax · approximately 3 min read
Probability Topics
Student Learning Outcomes
The student will use theoretical and empirical methods to estimate probabilities.
The student will appraise the differences between the two estimates.
The student will demonstrate an understanding of long-term relative frequencies.
Do the Experiment Count out 40 mixed-color candies, which is approximately one small bag’s worth. Record the number of each color in M05_ch03-tbl009 . Use the information from this table to complete M05_ch03-tbl010 . Next, put the candies in a cup. The experiment is to pick two candies, one at a time. Do not look into the cup as you pick them. The first time through, replace the first candy before picking the second one. Record the results in the With Replacement column of M05_ch03-tbl011 . Do this 24 times. The second time through, after picking the first candy, do not replace it before picking the second one. Then, pick the second one. Record the results in the Without Replacement column section of M05_ch03-tbl012 . After you record the pick, put both candies back. Do this a total of 24 times, also. Use the data from M05_ch03-tbl012 to calculate the empirical probability questions. Leave your answers in unreduced fractional form. Do not multiply out any fractions.
Note
G 2 = green on second pick, R 1 = red on first pick, B 1 = brown on first pick, B 2 = brown on second pick,
Discussion Questions
Why are the With Replacement and Without Replacement probabilities different?
Convert P (no yellows) to decimal format for both Theoretical With Replacement and for Empirical With Replacement. Round to four decimal places.
Theoretical With Replacement : P (no yellows) = _______
Empirical With Replacement: P (no yellows) = _______
Are the decimal values close ? Did you expect them to be closer together or farther apart? Why?
If you increased the number of times you picked two candies to 240 times, why would empirical probability values change?
Would this change (see Question 3) cause the empirical probabilities and theoretical probabilities to be closer together or farther apart? How do you know?
Explain the differences in what P (G 1 AND R 2 ) and P (R 1 |G 2 ) represent. Hint: Think about the sample space for each probability.
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