Exam 4: Basic Probability

If either A or B must occur they are called collectively exhaustive.

If two events are collectively exhaustive,what is the probability that both occur at the same time?

SCENARIO 4-3 A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or chicken.Of 200 respondents selected,75 were children and 125 were adults.120 preferred hamburger and 80 preferred chicken.55 of the children preferred hamburger. -Referring to Scenario 4-3,the probability that a randomly selected individual is an adult and prefers chicken is_____ .

If two events are mutually exclusive,what is the probability that one or the other occurs?

A company has 2 machines that produce widgets.An older machine produces 23% defective widgets,while the new machine produces only 8% defective widgets.In addition,the new machine produces 3 times as many widgets as the older machine does.What is the probability that a randomly chosen widget produced by the company is defective?

SCENARIO 4-6 At a Texas college,60% of the students are from the southern part of the state,30% are from the northern part of the state,and the remaining 10% are from out-of-state.All students must take and pass an Entry Level Math (ELM)test.60% of the southerners have passed the ELM,70% of the northerners have passed the ELM,and 90% of the out-of-staters have passed the ELM. -Referring to Scenario 4-6,the probability that a randomly selected student is not from southern Texas and has not passed the ELM is_____ .

If event A and event B cannot occur at the same time,then events A and B are said to be

Eleven freshmen are to be assigned to eleven empty rooms in a student dormitory.Each room is considered unique so that it matters who is being assigned to which room.How many different ways can those eleven freshmen be allocated?

SCENARIO 4-11 A sample of 300 adults is selected.The contingency table below shows their registration status and their preferred source of information on current events. -Referring to Scenario 4-11,if a randomly selected adult is a registered voter,what is the probability that he/she prefers to get his/her current information from the newspapers?

SCENARIO 4-2 An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying,and whether they did well or poorly on the midterm.The following result was obtained. -Referring to Scenario 4-2,the events "Did Well on Midterm" and "Did Poorly on Midterm" are

SCENARIO 4-5 In a meat packaging plant Machine A accounts for 60% of the plant's output,while Machine B accounts for 40% of the plant's output.In total,4% of the packages are improperly sealed.Also,3% of the packages are from Machine A and are improperly sealed. -Referring to Scenario 4-5,if a package selected at random came from Machine B,the probability that it is improperly sealed is_____ .

If two events are mutually exclusive and collectively exhaustive,what is the probability that one or the other occurs?

According to a survey of American households,the probability that the residents own 2 cars if annual household income is over $50,000 is 80%.Of the households surveyed,60% had incomes over $50,000 and 70% had 2 cars.The probability that the residents do not own 2 cars if annual household income is not over $50,000 is:

SCENARIO 4-8 According to the record of the registrar's office at a state university,35% of the students are freshman,25% are sophomore,16% are junior and the rest are senior.Among the freshmen,sophomores,juniors and seniors,the portion of students who live in the dormitory are,respectively,80%,60%,30% and 20%. -Referring to Scenario 4-8,if a randomly selected student does not live in the dormitory,what is the probability that the student is a junior or a senior?

Suppose A and B are independent events where P(A)= 0.4 and P(B)= 0.5.Then P (A or B)= .

SCENARIO 4-8 According to the record of the registrar's office at a state university,35% of the students are freshman,25% are sophomore,16% are junior and the rest are senior.Among the freshmen,sophomores,juniors and seniors,the portion of students who live in the dormitory are,respectively,80%,60%,30% and 20%. -Referring to Scenario 4-8,what is the probability that a randomly selected student is a junior or senior who lives in a dormitory?

Suppose A and B are events where P(A)= 0.4,P(B)= 0.5,and P (A and B)= 0.1.Then P(A|B)= .

Suppose A and B are events where P(A)= 0.4,P(B)= 0.5,and P (A and B)= 0.1.Then P (A or B)= .

SCENARIO 4-3 A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or chicken.Of 200 respondents selected,75 were children and 125 were adults.120 preferred hamburger and 80 preferred chicken.55 of the children preferred hamburger. -Referring to Scenario 4-3,the probability that a randomly selected individual is a child and prefers chicken is_____ .

The employees of a company were surveyed on questions regarding their educational background (college degree or no college degree)and marital status (single or married).Of the 600 employees,400 had college degrees,100 were single,and 60 were single college graduates.The probability that an employee of the company does not have a college degree is: