Exam 4: Probability

A market research firm is investigating the appeal of three package designs.The table below gives information obtained through a sample of 200 consumers.The three package designs are labelled A,B,and C.The consumers are classified according to age and package design preference. If one of these consumers is randomly selected,what is the probability that the person prefers design A and is under 25?

In a set of 15 aluminum castings,two castings are defective (D),and the remaining thirteen are good (G).A quality control inspector randomly selects three of the fifteen castings without replacement,and classifies each as defective (D)or good (G).The sample space for this experiment contains ___ elementary events.

Calculate conditional probabilities with various forms of the law of conditional probability,and use them to determine if two events are independent.

Abel Alonzo,Director of Human Resources,is exploring employee absenteeism at the Plano Power Plant.Ten percent of all plant employees work in the finishing department;20% of all plant employees are absent excessively;and 7% of all plant employees work in the finishing department and are absent excessively.A plant employee is selected randomly;F is the event "works in the finishing department;" and A is the event "is absent excessively." P(F|A)= ___.

Belinda Bose is reviewing a newly proposed advertising campaign.Based on her 15 years experience,she believes the campaign has a 75% chance of significantly increasing brand name recognition of the product.This is an example of assigning probabilities using the ___ method.

If the occurrence of one event precludes the occurrence of another event,then the two events are independent.

An analysis of personal loans at a local bank revealed the following facts: 10% of all personal loans are in default (D),90% of all personal loans are not in default (D΄),20% of those in default are homeowners (H | D),and 70% of those not in default are homeowners (H | D΄).If a personal loan is selected at random,P (D | H)= ___.

If two events are mutually exclusive,then the two events are also independent.

Given P (A)= 0.40,P (B)= 0.50,P (A $\cap$ B)= 0.15.Find P (B|A).

Given P(A)= 0.40,P(B)= 0.50,P(A $\cap$ B)= 0.15.Find P(A $\cup$ B).

A market research firms conducts studies regarding the success of new products.The company is not always perfect in predicting the success.Suppose that there is a 50% chance that any new product would be successful (and a 50% chance that it would fail).In the past,for all new products that ultimately were successful,80% were predicted to be successful (and the other 20% were inaccurately predicted to be failures).Also,for all new products that were ultimately failures,70% were predicted to be failures (and the other 30% were inaccurately predicted to be successes).What is the a priori probability that a new product would be a success?

Max Sandlin is exploring the characteristics of stock market investors.He found that sixty percent of all investors have a net worth exceeding $1,000,000;20% of all investors use an online brokerage;and 10% of all investors a have net worth exceeding $1,000,000 and use an online brokerage.An investor is selected randomly,and E is the event "net worth exceeds $1,000,000" and O is the event "uses an online brokerage." P(O $\cup$ E)= ___.

An experiment is a process that produces outcomes.

In a set of 10 aluminum castings,two castings are defective (D),and the remaining eight are good (G).A quality control inspector randomly selects three of the ten castings with replacement,and classifies each as defective (D)or good (G).The sample space for this experiment contains ___ elementary events.

Consider the following sample space,S,and several events defined on it.S = {Albert,Betty,Abel,Jack,Patty,Meagan},and the events are: F = {Betty,Patty,Meagan},H = {Abel,Meagan},and P = {Betty,Abel}.The complement of F is ___.

The table below provides summary information about students in a class.The sex of each individual and the major is given. If a student is randomly selected from this group,what is the probability that the student is a female who majors in accounting?

If the occurrence of one event does not affect the occurrence of another event,then the two events are mutually exclusive.

An automobile dealer wishes to investigate the relation between the gender of the buyer and type of vehicle purchased.Based on the following joint probability table that was developed from the dealer's records for the previous year,P (Female)= ___.

If X and Y are mutually exclusive,then ___.

An automobile dealer wishes to investigate the relation between the gender of the buyer and type of vehicle purchased.Based on the joint probability table below that was developed from the dealer's records for the previous year,P (Female $\cap$ SUV)= ___.