Exam 6: Probability

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} What is the probability that the patient has a benign tumor if he or she tests positive?

The first set of branches of a probability tree represent ____________________ probabilities.

An individual outcome of a sample space is called a(n)____________________ event.

Suppose P(A)= 0.50,P(B)= 0.40,and P(B|A)= 0.30. a.Find P(A and B). b.Find P(A or B). c.Find P(A|B).

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.

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(B and O).

P(A)+ P(B)= 1 for any events A and B that are mutually exclusive.

The conditional probability of event B given event A is denoted by P(A|B).

Bayes' Law is a formula for revising an initial subjective (prior)probability value on the basis of new results,thus obtaining a new (posterior)probability value.

If events A and B cannot occur at the same time,they are called mutually exclusive.

If P(A)= 0.35,P(B)= 0.45,and P(A and B)= 0.25,then P(A|B)is:

Posterior probability of an event is the revised probability of the event after new information is available.

If the outcome of event A is not affected by event B,then events A and B are said to be

If two events are mutually exclusive,their joint probability is ____________________.

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

Construction Bids ​ A construction company has submitted bids on two separate state contracts,A and B.The company feels that it has a 60% chance of winning contract A,and a 50% chance of winning contract B.Furthermore,the company believes that it has an 80% chance of winning contract A if it wins contract B. ​ ​ -{Construction Bids Narrative} What is the probability that the company will win both contracts?

A(n)____________________ is a collection or set of one or more simple events in a sample space.

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

If two events are independent,what is the probability that they both occur?

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 3 vehicles were involved,what proportion of accidents involved alcohol?