# Probability

CPSMA 3913 Project Module 3: Probability

1. Create your own sample space, compute probabilities and simulate selecting items from it.

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(a) Create a sample space with three or more simple events. Assign a probability to each item. Show that the axioms of probability hold under this assignment.

(b) Create a compound event that uses some of the simple events.

(c) Compute the probability of a union and an intersection of your events.

(d) Compute both conditional probabilities of two events. Make sure to explain what they are in words. Apply Bayes’ theorem to verify your result.

(e) Compute the probability of the complement of an event.

(f) Simulate a simple occurrence of your sample space 10 times. Pick an event, does the simulation give you exactly the same probability as your assignment? Explain why or why not.

2. Be sure to comment on the following:

(a) Describe your findings in words.

(b) If you were unable to code something discuss what the difficulty was and why doing it by hand was easier.

(c) Discuss how simulation might be different than your ideal sample space.

The first report will be graded by the following criteria:

� Report Style – 5 points. Your report contains a title, author’s name, class it is for, and instructor’s name.

� Clean Code- 5 points. Functions and variables are defined with descriptive names. Code can be interpreted with minimal effort.

� Probability – 5 points. Probability makes sense. Explanation is given of computations.

� Simulation – 5 points. Simulation works correctly and gives reasonable results. Those results are interpreted.

� Writing Quality – 5 point. The paper is readable, clearly written and contains a single voice. There are few, if any, grammatical or spelling errors and they do not interfere with the clarity of the paper.

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