Exam 6: Probability

Bayes' Law can be used to calculate posterior probabilities,prior probabilities,as well as new conditional probabilities.

If A and B are two independent events with P(A)= 0.9 and P(B|A)= 0.5,then P(A and B)= 0.45.

GPA and Class A college professor classifies his students according to their grade point average (GPA)and their class rank.GPA is on a 0.0-4.0 scale,and class rank is defined as the under class (freshmen and sophomores)and the upper class (juniors and seniors).One student is selected at random. ​ ​ -{GPA and Class Narrative} If the GPA of the student selected is over 3.0,what is the probability that the student is in the lower class?

Business Majors Suppose 30% of business majors major in accounting.You take a random sample of 3 business majors. ​ ​ -{Business Majors Narrative} What is the chance that exactly one majors in accounting?

Which of the following is equivalent to P(B)if A and B are independent?

No matter which approach was used to assign probability (classical,relative frequency,or subjective)the one that is always used to interpret a probability is the ____________________ approach.

Club Members A survey of a club's members indicates that 50% own a home,80% own a car,and 90% of the homeowners who subscribe also own a car. ​ ​ -{Club Members Narrative} What is the probability that a club member owns a car or a house,or both?

GPA and Class A college professor classifies his students according to their grade point average (GPA)and their class rank.GPA is on a 0.0-4.0 scale,and class rank is defined as the under class (freshmen and sophomores)and the upper class (juniors and seniors).One student is selected at random. ​ ​ -{GPA and Class Narrative} If the student selected is in the upper class,what is the probability that her GPA is between 2.0 and 3.0?

Hobby Shop Sales Sales records of a hobby shop showed the following number of radio controlled trucks sold weekly for each of the last 50 weeks. ​ ​ -{Hobby Shop Sales Narrative} What is the probability of selling between 1 and 3 (inclusive)trucks in any given week?

If A and B are ____________________ events,the joint probability of A and B is the product of the probabilities of those two events.

Club Members A survey of a club's members indicates that 50% own a home,80% own a car,and 90% of the homeowners who subscribe also own a car. ​ ​ -{Club Members Narrative} What is the probability that a subscriber owns both a car and a house?

The intersection of two events A and B is the event that occurs when both A and B occur.

If P(B)= .7 and P(B|A)= .4,then P(A and B)must be .28.

Messenger Service ​ Three messenger services deliver to a small town in Oregon.Service A has 60% of all the scheduled deliveries,service B has 30%,and service C has the remaining 10%.Their on-time rates are 80%,60%,and 40% respectively.Define event O as a service delivers a package on time. ​ ​ -{Messenger Service Narrative} Calculate P(C and O).

Marital Status An insurance company has collected the following data on the gender and marital status of 570 customers. Suppose that a customer is selected at random. ​ ​ -{Marital Status Narrative} Find the probability that the customer selected is a married female.

GPA and Class A college professor classifies his students according to their grade point average (GPA)and their class rank.GPA is on a 0.0-4.0 scale,and class rank is defined as the under class (freshmen and sophomores)and the upper class (juniors and seniors).One student is selected at random. ​ ​ -{GPA and Class Narrative} What is the probability that the student is in the lower class?

Messenger Service ​ Three messenger services deliver to a small town in Oregon.Service A has 60% of all the scheduled deliveries,service B has 30%,and service C has the remaining 10%.Their on-time rates are 80%,60%,and 40% respectively.Define event O as a service delivers a package on time. ​ ​ -{Messenger Service Narrative} If a package was delivered 40 minutes late,what is the probability that it was service A?

The outcomes of a sample space must be ____________________ and ____________________.

Messenger Service ​ Three messenger services deliver to a small town in Oregon.Service A has 60% of all the scheduled deliveries,service B has 30%,and service C has the remaining 10%.Their on-time rates are 80%,60%,and 40% respectively.Define event O as a service delivers a package on time. ​ ​ -{Messenger Service Narrative} If a package was delivered on time,what is the probability that it was service B?

In the scenario of Bayes' Law,P(A|B)is a(n)____________________ probability,while P(B|A)is a posterior probability.