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 labeled A,B,and C. The consumers are classified according to age and package design preference. If one of these consumers is randomly selected and is under 25,what is the probability that the person prefers design A?

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

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). For any randomly selected new product,what is the probability that the market research firm would predict that it would be a success?

The department in which you work in your company has 24 employees.A team of 3 employees must be selected to represent the department at a companywide meeting in the headquarters of the company.How many different teams of 3 can be selected?

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)= _______.

Let F be the event that a student is enrolled in a finance course,and let S be the event that a student is enrolled in a statistics course. It is known that 40% of all students are enrolled in a finance course and 35% of all students are enrolled in statistics. Included in these numbers are 15% who are enrolled in both statistics and finance. A student is randomly selected,and it is found that the student is enrolled in finance. What is the probability that this student is also enrolled in statistics?

A market research firm 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). If the market research predicted that the product would be a success,what is the probability that it would actually be a success?

Assigning probability 1/52 on drawing the ace of spade in a deck of cards is an example of assigning probabilities using the ________________ method

Suppose that your company is sending invitations to its 50 most important clients for an end-of-the-year event where a new product will be exhibited.These are printed invitation cards mailed through USPS,and each card is personalized with the name of the corresponding client.You realize that the cards have been accidentally shuffled before placing them in the envelopes.What is the probability that only one card is in the wrong envelope?

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

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 (H $\cap$ D')= ___________.

A recently published study shows that 50% of Americans adults take multivitamins regularly.Another recent study showed that 20.6% of American adults work out regularly.Suppose that these two variables are independent.The probability that a randomly selected American adult takes multivitamins regularly and works out regularly is _______.

Given that two events,A and B,are independent,if the marginal probability of A is 0.6,the conditional probability of A given B will be 0.4.

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}. F $\cap$ H is ___________.

Suppose 5% of the population have a certain disease.A laboratory blood test gives a positive reading for 95% of people who have the disease and 10% positive reading of people who do not have the disease.What is the probability that a randomly selected person has the disease given that this person is testing positive?

It is known that 20% of all students in some large university are overweight,20% exercise regularly and 2% are overweight and exercise regularly.What is the probability that a randomly selected student is either overweight or exercises regularly or both?

There are three companies that produce a critical electronic navigation component (ENC)used in the aerospace industry.These companies are Alice Manufacturing,Byte International,and Cognizant Technologies.Alice makes 85% of the ENCs,Byte makes 10%,and Cognizant makes the remaining 5%.The ENCs made by Alice have a 2.5% rate of defects,the ones made by Byte have a 4.0% rate of defects,and the ones made by Cognizant have a 6% rate of defects.If an ENC is randomly selected from the general population of ENCs,the probability that it was made by Alice is _______.If this ENC is later tested and found to be defective,the probability that it was made by Alice is _______.

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 labeled A,B,and C. The consumers are classified according to age and package design preference. Are "B" and "25 or older" independent and why or why not?

The number of different committees of 2 students that can be chosen from a group of 5 students is

The department in which you work in your company has 10 employees: 10 women and 14 men.A team of anywhere from one employee up to 9 employees must be chose to attend a meeting at the company's headquarters.How many different teams can be selected?