Mrs. Conway, AP Statistics Name: ______

Freeman High School Date: ______

Probability Review

Use this information to answer the following questions:

As shown in the accompanying diagram, a square target with a

length of 3 feet has a circular bull’s eye with a

radius of 1 foot.

1. If an arrow randomly hits the target, what is the probability that the

arrow hits the bull’s eye? That the arrow does not hit the bull’s eye?

2. If three arrows randomly hit the target, what is the probability that all three arrows hit the bull’s eye?

3. If three arrows randomly hit the target, what is the probability that the first two arrows hit the bull’s eye and the third one does not hit the bull’s eye?

4. If three arrows randomly hit the target, what is the probability that two arrows hit the bull’s eye and one does not?

5. If three arrows randomly hit the target, what is the probability that at least two arrows hit the bull’s eye?

6. All bags entering a research facility are screened. Ninety-seven percent of the bags that contain forbidden material trigger an alarm. Fifteen percent of the bags that do not contain forbidden material also trigger the alarm. If 1 out of every 1,000 bags entering the building contains forbidden material, what is the probability that a bag triggers the alarm will actually contain forbidden material.

7. Suppose your shelf contains four mathematics textbooks and only two English textbooks (we all know that the study of mathematics is far superior to the study of English, although both are very important). You randomly choose two books. What is the probability that one is a mathematics book and one is an English book?

8. The probability that event A occurs is 0.5, the probability that even B occurs is 0.3 and the probability that both occur is 0.11. What is the probability that event A or event B will occur?

9. The probability that event A occurs is 0.5, the probability that even B occurs is 0.3. If A and B are independent events, then what is the probability that event A or event B will occur?

10. The probability that event A occurs is 0.5, the probability that even B occurs is 0.3. If A and B are mutually exclusive events, then what is the probability that event A or event B will occur?