Exam 4: Basic Probability

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 someone from northern Texas who has not passed the ELM is .

A debate team of 4 is to be chosen from a class of 35.There are two twin brothers in the class.How many possible ways can the team be formed which will include only one of the twin brothers?

SCENARIO 4-9 A survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their non-cash compensation packages.For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their noncash compensation packages to their board members. -Referring to Scenario 4-9, set up a contingency table.

If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur?

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:

There are only 4 empty rooms available in a student dormitory for eleven new freshmen.Each room is considered unique so that it matters who is being assigned to which room.How many different ways can those 4 empty rooms be filled one student per room?

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 .

The closing price of a company's stock tomorrow can be lower, higher or the same as today's closing price.After evaluating all the information available on the company's fundamentals and the economic environment, an analyst has determined that the probability that tomorrow's closing price will be higher than today's is determined to be 25%.This is an example of using which of the following probability approach?

There are 10 finalists at a national dog show.How many different orders of finishing can there be for all the 10 finalists?

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 proportion of the students do not live in a dormitory?

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