1. If you flip a single coin four times, what is the probability of getting 3 tails?

2. Being careful to follow (and clearly identify) the four steps in the online *Course Content*, calculate the probability of randomly drawing two cards consisting of a red three, and either any Jack or a red seven (in any order) when randomly drawing two cards from a standard deck without replacement.

3. Being careful to follow (and clearly identify) the four steps in the online *Course Content*, calculate the following probability: What is the probability of rolling a 4 in a single roll of two dice?

4. You are scheduling classes for next semester and need to take exactly one course from each of the three categories below. Draw a possibility tree to show all your possible schedules. HINT: you might want to investigate Word’s Insertà SmartArtà Hierarchy drawing features.

1. IST 230, Math 110

2. Biol, Psych, Music

3. IST 451, IST 461

5. Six musicians need to be seated around a table for lunch. The particular seat at which a given person sits doesn’t matter, but the relative arrangement of the people does (since some of them compete with one another for the same venues). How many ways can you seat the musicians?

6. How many ways can you arrange the letters in the word PROBLEM?

7. How many ways can you arrange the letters in the word “EXPRESS”?

8. A is a set with 70,000 elements; B is a set with 2,000 elements. How many elements are in A x B?

9. ways can you arrange 5 of the 11 students for the event (HINT: the order of the students matters)?

You need to select 5 IST students from a class of 11 and line them up for commencement. How many different

10. of digits permitted)?

A PIN can be either 4 or 5 characters long. How many PINs can you make from the digits 1 – 9 (with repetition

11. 36 students signed up for chorus, 50 students signed up for band, and 23 students signed up for both. How many students are participating in one or more of these activities?

12. You need to select 5 IST students from a group of 8 to represent Penn State at a banquet. How many different ways can you choose 5 of the 8 students for the group (HINT: the order of the students does *not* matter)?

13. A group of 11 students consists of 6 IST majors and 5 Music majors. How many ways can you form a 5-student committee consisting of 2 IST majors and 3 Music majors?

14. The probability of falling asleep while studying for IST 230 is 0.63. What is the probability of *not* falling asleep while studying for IST 230?

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