Exam 5: Probability

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

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

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

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

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?

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?

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.

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

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

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

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?

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?

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?

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.

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?

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?

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.

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?

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

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