Chapter 6: Probability

Transcription

1 Chapter 6: Probability Name 1. A small ferryboat transports vehicles from one island to another. Consider the chance experiment where the type of vehicle -- passenger (P) or recreational (R) vehicle -- is recorded for each of the next two vehicles that arrive at the dock. a) List all the events in the sample space. b) Using the sample space in part (a), list the outcomes for each of the following events A: B: C: A = the event that both vehicles are passenger cars B = the event that both vehicles are of the same type C = the event that there is at least one passenger car c) Display the sample space in the form of a tree diagram. Page 1 of 8

2 2. In a survey of airline travelers, passengers were selected at random from those who were traveling alone in the coach section. The selected passengers were asked if they were bothered by a seatmate of the opposite gender using the common armrest. The table below contains data gathered in that study. Discontentment Felt When Seat-mate Used Common Armrest: Males and Females Bothered Not bothered Females Males Suppose one of these passengers is to be randomly selected for a follow-up interview. Use the information in the table to answer the questions below. In showing your work, define and use appropriate notation. a) What is the probability that the selected passenger is female? b) What is the probability that the selected passenger is female or is bothered? c) What is the probability that the selected passenger is be male and is not bothered? Page 2 of 8

3 3. In the survey of travelers described in problem 2, passengers were also classified by age: Discontentment Felt When Seat-mate Used Common Armrest: Males and Females by Age Bothered Not bothered Totals Females under Males under Females over Males over Totals Suppose one of these passengers is to be randomly selected. Calculate the probability that: a) The selected passenger is under 40, given that the passenger is female. b) The selected passenger is bothered, given that the passenger is over 40. c) The selected passenger is male and over 40. Page 3 of 8

4 4. Students in two classes of upper-level mathematics were classified according to class standing and gender, resulting in the following table. Distribution of students: Advanced math Jr Sr Males Females A student from one of these two classes will be selected at random. Define events A, B, and C as follows: A = the event that the selected student is a female B = the event that the selected student is a male C = the event that the selected student is a senior. For each pair of events in the following table, indicate whether the two events are disjoint and/or independent by putting a Y or N in each of the cells. Y = Yes, N = No A, B B, C A, C Disjoint Independent Page 4 of 8

5 5. Suppose 70% of orders on a particular website are shipped to the person who is making the order and the remaining 30% are shipped to people other than the person placing the order. Gift wrapping is requested for 60% of the orders being shipped to other people, but for only 10% of orders shipped to the person making the order. a) What is the probability that a randomly selected order will be gift wrapped and sent to a person other than the person making the order? b) What is the probability that a randomly selected order will be gift wrapped? c) Is gift-wrapping independent of the destination of the gift? Justify your response statistically. Page 5 of 8

6 6. Black bears (Ursus americanus) have a tendency to wander for food, and they have a high level of curiosity. These characteristics will sometimes get them into trouble when they travel through national parks. When they become "nuisances," the Park Service transplants them if possible to other areas. The outcomes of such transplants in Glacier National Park over a 10-year period are given in the table below. Transplanted Bear Table Male Female Totals Successful Returned to capture area Nuisance in another area Killed outside of park Totals a) If a bear is randomly selected from the 153 bears in the sample, what is the probability it is male and became a nuisance in another area after relocation. b) If a bear is randomly selected from the 153 bears in the sample, what is the probability that it is female or was successfully transplanted. Page 6 of 8

7 c) If a bear is randomly selected from the bears in the samle, what is the probability that it returned to the capture area, given that it is a female? d) After combining the above data with other National Parks, officials estimated that only about 22% of black bears in all parks become enough of a nuisance to be transplanted. They further estimate that 84% of nuisance bears are male, and fifty percent of non-nuisance bears are females. If a randomly selected bear were observed to be a male, what is the probability it would be enough of a nuisance to be transplanted? Page 7 of 8

8 7. At Thomas Jefferson High School students are heavily involved in extra-curricular activities. Suppose that a student is to be selected at random from this school. Let the events A, M, and S be defined as follows, with the probabilities listed: A = student is active in the performing arts: P(A) = 0.20 M = student is active in vocal or instrumental music: P(M) = 0.32 S = student is active in sports: P(S) = 0.35 PA ( Ç M) = 0.18; PA ( Ç S) = 0.07; PM ( S) = 0.30 Calculate each of the following (show your work): a) PAM ( ) b) PA ( È M) c) PM ( Ç S) Page 8 of 8