Exam 6: Probability

A conditional probability of A given B is written in probability notation as ____________________.

If either event A or event B must occur, they are called mutually exclusive.

Suppose A and B are two mutually exclusive events for which P(A) = 0.30 and P(B) = 0.40. a. Find P(A and B). b. Find P(A or B). c. Are A and B independent events? Explain using probabilities.

The collection of all the possible outcomes of a random experiment is called a sample space.

If P(A) = .30, P(B) = .60, and P(A and B) = .20, then P(A|B) = .40.

Tea and Seltzer Suppose 55 percent of adults drink tea, 45 percent drink seltzer, and 10 percent drink both. -{Tea and Seltzer Narrative} What is the probability that a randomly chosen adult drinks seltzer or tea 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} What is the probability that the student is in the lower class?

The probability of the intersection of two events A and B is denoted by P(A and B) and is called the:

Tea and Seltzer Suppose 55 percent of adults drink tea, 45 percent drink seltzer, and 10 percent drink both. -{Tea and Seltzer Narrative} What is the probability that a randomly chosen adult doesn't drink tea or seltzer?

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 at least two trucks in any given week?

If you roll a balanced die 50 times, you should expect an even number to appear:

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 C?

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 C?

Drunk Drivers Six hundred accidents that occurred on a Saturday night were analyzed.Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.The numbers are shown below: -{Drunk Drivers Narrative} If alcohol was not involved, what proportion of the accidents were single vehicle?

Cysts After researching cysts of a particular type, a doctor learns that out of 10,000 such cysts examined, 1,500 are malignant and 8,500 are benign.A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not).The doctor has discovered the same type of cyst in a patient. -{Cysts Narrative} In the absence of any test, what is the probability that the cyst is malignant?

Cysts After researching cysts of a particular type, a doctor learns that out of 10,000 such cysts examined, 1,500 are malignant and 8,500 are benign.A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not).The doctor has discovered the same type of cyst in a patient. -{Cysts Narrative} In the absence of any test, what is the probability that the cyst is benign?

Equity Loan Rates A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan, based on past records. -{Equity Loan Rates Narrative} If a bank is selected at random from this distribution, what is the probability that the interest rate charged on a home loan exceeds 7.0%?

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?

Drunk Drivers Six hundred accidents that occurred on a Saturday night were analyzed.Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.The numbers are shown below: -{Drunk Drivers Narrative} If multiple vehicles were involved, what proportion of accidents involved alcohol?

If P(A and B) = 1, then A and B must be mutually exclusive.