To review these concepts, go to Basic Ideas in Probability Study Guide.

**Basic Ideas in Probability Practice Questions**

**Practice**

A movie theatre is showing four different movies at any one time. On a given night, one of the theatre's customers is selected at random, and the movie he attends is observed.

- Give the sample space.
- List all events.
- The customer went to the third movie.Which event(s) has (have) occurred?
- Are the outcomes for this random experiment equally likely?

Seniors at a high school have the opportunity to choose several elective courses, including photography and drawing. The probability that a randomly selected senior is taking photography is 0.50 and the probability that a randomly selected senior is taking drawing is 0.30. The probability that a randomly selected senior is taking both classes is 0.10.

- What is the probability that a randomly selected senior is taking photography or drawing?
- What is the probability that a randomly selected senior is not taking photography?
- What is the probability that a randomly selected senior is taking neither photography nor drawing?

A high school athletic director wanted to know whether participation in high school sports differed with grade. Using school records, he determined how many students in each grade did not play any sport and how many played at least one sport. The results are shown in Table 9.2.

Let *P* = the event that the student plays at least one high school sport, *A* = the event that the student is a freshman, *B* = the event that the student is a sophomore, *C* = the event that the student is a junior, and *D* = the event that the student is a senior.

- What is the probability that a randomly selected student at this high school plays at least one high school sport?
- What is the probability that a randomly selected student is an upperclassman (junior or senior)?]
- What is the probability that a randomly selected student is a junior who plays at least one high school sport?
- What is the probability that a randomly selected student plays at least one high school sport given that he or she is a junior?
- Is the probability of a student playing at least one high school sport independent of he or she being a junior?
- The staff at a large high school is 35% male and 65% female.When asked if they liked the cafeteria food at the high school, 67% of the men on staff said they did, and 59% of the women on staff said they liked the food.What is the probability that a randomly selected staff member at the high school likes the school's cafeteria food?
- Suppose that, for the same high school mentioned in the previous practice problem, we select a staff member at random and determine that this person likes the cafeteria food.What is the probability that the staff member is a man?

**Solutions**

- S = {1, 2, 3, 4), where 1, 2, 3, and 4 each represent one of the four different movies showing at the theater.
- There are 2
^{4}events: Ø, {1}, {2}, {3}, {4}, {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}, {1,2,3}, {1,2,4}, {1,3,4}, {2,3,4},*S* - {3}, {1,3}, {2,3}, {3,4}, {1,2,3}, {1,3,4}, {2,3,4},
*S* - No, because one movie might be more popular than another movie showing at the theater.
- 0.70
- 0.50
- 0.30
- 0.52
- 0.44
- 0.10
- 0.43
- No,
*P*(*P*) = - 0.618
- 0.379

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