3.1 Exercise 7

In a particular college class, there are both men and women students. Some students have long hair and some students have short hair. Write the symbols for the probabilities of the events for parts a through j. (Note that you cannot find numerical answers here. You were not given enough information to find any probability values yet; concentrate on understanding the symbols.)

• Let W be the event that a student is a woman.
• Let M be the event that a student is a man.
• Let S be the event that a student has short hair.
• Let L be the event that a student has long hair.

1. The probability that a student does not have long hair.
2. The probability that a student is a man or has short hair.
3. The probability that a student is a woman and has long hair.
4. The probability that a student is a man, given that the student has long hair.
5. The probability that a student has long hair, given that the student is a man.
6. Of all the women students, the probability that a student has short hair.
7. Of all students with long hair, the probability that a student is a woman.
8. The probability that a student is a woman or has long hair.
9. The probability that a randomly selected student is a man with short hair.
10. The probability that a student is a woman.