### MATH 113: Theoretical Probability

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The purpose of this worksheet is to practice calculating theoretical probabilities using the methods described in section 14.4 of the textbook. The first set of questions deals with the experiment "roll two six sided dice and add the result". There's a nice diagram at the bottom of page 781 illustrating the 36 possible outcomes of this experiment.

We could define event A to be the outcome in which the sum of the dice is 7 (for example) and then compute P(A), but instead we'll just write P(7) for this event. Read through this whole sheet before starting and ask any questions you have about the event whose probability is being calculated.

1. Calculate P(3) and P(6).

2. Calculate P(3 or 12)

3. Which is more likely, that you will roll a 3 or 12 or that you will roll a 6?

4. What is the probability of getting an odd number?

5. What is the probability of getting an odd number or a 6?

6. What is the probability of getting an odd number or a number greater than (but not equal to) 8?

7. What is the probability of getting an odd number and a number greater than (but not equal to) 8?

8. If you know that the outcome is greater than 8, what is the probability that it is odd?

9. Use complementary probabilities to calculate the probability of rolling a number greater than (but not equal to) 3.

In the next portion of this worksheet you will use permutations and combinations to calculate probabilities.

Suppose the BSU math club has 8 female members and 5 male members, and that four of the female members are named Jessica.

1. How many different ways are there to elect 3 officers for the club: President, Vice President and Treasurer?

2. How many different ways are there to form a committee of 3 club members?

3. Three students are selected to serve on a committee. What is the probability that they are all named Jessica?

4. What is the probability that the President, Vice President and Treasurer are all named Jessica?

Bonus: What is the probability that all the officers are male or that all are named Jessica?