Deck 5: Probability

Question 1

The collection of possible outcomes of a chance experiment is called thesample space of the experiment.

Answer 1

True

Question 2

The event "A or B" consists of all of the outcomes that are in both of theevents.

Answer 2

False

Question 3

As discussed in the text, the classical approach to probability has a serious limitationthat is overcome by the relative frequency approach. What is the limitation?

Answer 3

The classical approach is only appropriate when the outcomes of the experiment are equally likely outcomes.

Question 4

Anna is an engineer on vacation with a problem. S he is driving in Halifax, NovaScotia, and is stopped at an intersection. She could drive to Wolfville, Truro, orAntigonish. She does not have a preference, and decides make her decision byflipping two coins. If two heads appear, she will go to Wolfville, if two tails she willgo to Antigonish. What is the probability she will go to Truro?

Question 5

Anna is a child who has just turned 2 years old, and she has entered the "terribletwo's" stage of human development. She has discovered that if she drops her spoonon the floor, her parents will pick it up and return it to her. By actual count halfwaythrough her second year, there have been 900 spoon retrievals. Out of these, 315times the spoon has landed in the "up" position on the floor. Based on this long seriesof observations, what is the estimated probability that her 901st spoon drop will landin the "up" position?

Question 6

The probability of an event E can always be computed using the formula,

Question 7

A chance experiment is the process of making an observation when thereis uncertainty concerning which of two or more possible outcomes willresult.

Question 8

Moosy-Woosy Airlines flies between Moose Bay and Moose Lake Alaska. In manyairports, nearby flocking birds can present problems during takeoffs and landings. InAlaska, the problem is moose. If a moose is spotted in the immediate area of therunway, a takeoff or landing must be delayed until the moose is very carefullyescorted away. Of the 1200 takeoffs and landings in a recent 12-month period atMoose Bay, there were 75 moose delays. Based on this long series of observations,what is the estimated probability that the 1201st takeoff or landing attempt will bedelayed by a moose sighting?

Question 9

As discussed in the text, the classical approach to probability has a serious limitationthat is overcome by the relative frequency approach. What is the limitation?

Question 10

In a few sentences, define the following terms:
a) Event
b) Chance experiment

Question 11

Experimental studies in psychology use blinding to prevent researchers from biasingtheir measurements of subjects in the study. In a study of a psychotherapeuticintervention, a blinded clinician was asked to guess what treatment each subjectreceived. Data from that experiment are shown below. Suppose a subject is to bechosen at random from the subjects in this study.
a) What is the probability that the clinician made a correct guess for the selectedsubject?
b) What is the probability the selected subject will have had therapy?
c) What is the probability the selected subject will be one for whom the cliniciancorrectly guessed had therapy?
d) What is the probability the selected subject will be one for whom the clinicianguessed correctly or who received the placebo treatment?
e) What is the probability the selected subject will be one for whom the clinicianguessed correctly and who received the placebo treatment?
f) In a few sentences, explain why the probabilities calculated in parts (d) and (e)differ.

Question 12

Understanding attitudes of humans towards wildlife is an important step in learning how to work with people on wildlife issues. Coyotes have expanded their range throughout the continental United States, even in the Washington, DC area. The data below are from a survey of George Mason University undergraduate students.


Suppose a newspaper decides to select one of these students at random for an interview.

-What is the probability that the selected student dislikes coyotes somewhat?

Question 13

It is possible for two mutually exclusive events to be independent.

Question 14

Two events are said to be mutually exclusive if they can't occur at thesame time.

Question 15

Arctic Plains Planes Airlines flies in Alaska between Prudhoe Bay and Deadhorse.APPA has only one small plane, and passengers have a choice between sitting in oneof two first class seats, one of four second class seats, and the co-pilot's seat. (APPAairlines also has only one pilot.) If the seats are assigned at random, what is theprobability that a passenger will be assigned a second class seat?

Question 16

In a few sentences, define the following terms:
a) Simple event
b) Sample space

Question 17

In a few sentences, explain the difference between an event, A, and the complement ofevent A.

Question 18

An event, by definition, consists of exactly one outcome.

Question 19

Experimental studies use blinding to prevent researchers from biasing theirmeasurements of the subjects. In a study of a drug intervention, a clinician who was"blinded" was asked to guess what treatment each subject received. Data from thatexperiment are shown below. Suppose a person is to be chosen at random from thesubjects in this study.
a) What is the probability that the clinician made a correct guess for the selectedsubject?
b) What is the probability the selected subject received the drug treatment?
c) What is the probability the selected subject will be one for whom the cliniciancorrectly guessed as having received drug treatment?
d) What is the probability the selected subject will be one for whom the clinicianguessed correctly or who received the standard treatment?
e) What is the probability the selected subject will be one for whom the clinicianguessed correctly and who received the standard treatment?
f) In a few sentences, explain why the probabilities calculated in parts (d) and (e)differ.

Question 20

In a few sentences, describe the difference between the intersection of two events andthe union of two events

Question 21

At Beth & Mary's Ice Cream Emporium customers always choose one topping tosprinkle on their ice cream. The toppings are classified as either candy (C) or fruit(F) toppings. Consider the chance experiment where the choice of toppings -- (C) or (F) -- is recorded for each of the next two customers who order ice cream.
a) List all the outcomes in the sample space.
b) Using your sample space in part (a), list the outcomes in each of the following events.
A = the event that both customers pick a candy topping
B = the event that both customers pick the same type of topping
C = the event that at least one customer picks a candy topping

Question 22

Understanding attitudes of humans towards wildlife is an important step in learning how to work with people on wildlife issues. Coyotes have expanded their range throughout the continental United States, even in the Washington, DC area. The data below are from a survey of George Mason University undergraduate students.


Suppose a newspaper decides to select one of these students at random for an interview.

-What is the probability that the selected student is male?

Question 23

Like many professionals, the clergy in mainline Protestant churches have pensionplans. Due to the nature of the ministry, investment strategies may involve what areknown as "screens." Screens are rules that prevent a pension fund administrator frominvesting in corporations that are involved with, for example, alcohol, gambling,tobacco and weapons of mass destruction. Ministers may elect to invest in two broadcategories: "regular" and "social purpose" funds, which would typically use screensin their investment strategy. The use of screens may reduce their monthly benefit atretirement.

The data below are from a survey of ministers about their support in principle for theuse of such screens. Each minister asked if the screens should be applied to theregular funds, the social purpose funds, both, or neither. The ministers were alsoclassified by the current percentage of their investments in the social purpose funds:0%, 10 - 59%, 60% or greater.

a) What is the probability that a minister selected at random from those whoparticipated in the survey was uncertain about the use of screens?
b) What is the probability that a minister selected at random from those whoparticipated in the survey was in the 60+% group and supported the use of screensfor social purpose funds only?
c) What is the probability that a minister selected at random from those whoparticipated in the survey felt the screens should be used for social purpose fundsonly or for both social purpose and regular funds, given that they were in the 10-59% group?
d) What is the probability that a randomly selected "uncertain" minister would be inthe 0% group?

Question 24

All statistics teachers love Girl Scout Cookies. The number of boxes of Girl Scoutcookies a statistics teacher orders is (of course) determined by the roll of a 4-sidedfair die. If a one appears, 6 boxes are ordered; if any other number appears, 2 boxesare ordered.
a) What is the probability that a statistics teacher places an order for 2 boxes of GirlScout cookies?
b) What is the probability that two statistics teachers (each rolling a die to determinethe number of boxes ordered) will each order 6 boxes each?
c) What is the probability that for two statistics teachers (each rolling a die todetermine the number of boxes ordered), the first will order 6 boxes and thesecond will order 2 boxes?
d) What is the probability that for two statistics teachers (each rolling a die todetermine the number of boxes ordered), exactly one will order 6 boxes?

Question 25

First graders at an elementary school were classified according to whether they werethe first born child in the family or not, and also whether both parents worked outsidethe home. This resulted in the accompanying table. Suppose that one of these students is selected at random. Define events A, B, and C as follows:
A = the event that the selected student is a first born
B = the event that the selected student's parents both work outside the home
C = the event that the selected student has older siblings

For each pair of events in the following table, indicate whether the two events are disjointand/or independent by putting a Y or N in the appropriate cells.

Question 26

The adult diamond python (Morelia spilota), an Australian snake, is about 3 feet long.In a multi-year study of the habitats of these creatures, 997 were captured. Thefollowing table displays the capture locations of these snakes by season of the yearand habitat. The "other" category includes trees, logs, rocks, open ground, and underfiltering cover such as shrubs.
Suppose one of these diamond pythons is selected at random.Calculate the probability that:
a) The selected diamond python was captured in a building, given that it wascaptured in the spring.
b) The selected diamond python was captured somewhere other than in a buildinggiven that it was captured in the spring or summer.
c) The selected diamond python was captured in a building in the summer.

Question 27

In November 2002, Janet Napolitano, a Democrat, was elected Governor of Arizona,defeating Republican Matt Salmon and Independent Richard Mahoney. This was asomewhat surprising outcome, since there are more registered Republicans thanDemocrats in the state. The table below presents data from a survey of a sample ofvoters in the election. The candidate supported by the voter is represented by therows, and the party affiliation of the voter is represented by the columns. Supposethat one of these voters is selected at random. Use the information in the table toanswer the questions below.
a) What is the probability that the selected voter voted for Napolitano?
b) What is the probability that the selected voter is a registered Democrat?
c) What is the probability that the selected voter voted for Napolitano, given that theselected voter is a Democrat?
d) A local reporter, commenting on this election, said, "Napolitano won because sheattracted a larger share of crossover voters." (A crossover voter is one who votesdifferently than his or her registration category. For example, a Democrat partymember voting Republican, or an Independent voting for a Democrat candidatewould be crossover voters). What is the probability that the selected voter votedfor Napolitano, given that he or she is a crossover voter?

Question 28

Understanding attitudes of humans towards wildlife is an important step in learning how to work with people on wildlife issues. Coyotes have expanded their range throughout the continental United States, even in the Washington, DC area. The data below are from a survey of George Mason University undergraduate students.


Suppose a newspaper decides to select one of these students at random for an interview.

-What is the probability that the selected student is male, given that he likes coyotesvery much?

Question 29

Understanding attitudes of humans towards wildlife is an important step in learning how to work with people on wildlife issues. Coyotes have expanded their range throughout the continental United States, even in the Washington, DC area. The data below are from a survey of George Mason University undergraduate students.


Suppose a newspaper decides to select one of these students at random for an interview.

-What is the probability that the selected student dislikes coyotes very much, giventhat she is a female?