Exam 4: Basic Probability

SCENARIO 4-1 Mothers Against Drunk Driving is a very visible group whose focus is to educate the public about the harm caused by drunk drivers.A study was recently done that emphasized the problem we all face with drinking and driving.Four 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: -Referring to Scenario 4-1, given alcohol was involved, what proportion of accidents involved a single vehicle?

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

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?

An investment consultant is recommending a certain class of mutual funds to the clienteles based on its exceptionally high probability of gain.It is an unethical practice not to also recommend a class of mutual funds with an exceptionally high probability of loss.

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

If two equally likely events A and B are collectively exhaustive, what is the probability that event A occurs?

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

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?

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 annual household income is over $50,000 if the residents of a household own 2 cars is:

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 an adult is selected at random, what is the probability that he/she is a not a registered voter or does not prefer to get his/her current information from the internet?

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.

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, if a randomly selected student is not from out-of-state, the probability the student has passed the ELM is ________.

A survey of banks revealed the following distribution for the interest rate being charged on a home loan (based on a 30-year mortgage with a 10% down payment)on a certain date in the past. If a bank is selected at random from this distribution, what is the chance that the interest rate charged on a home loan will exceed 3.49%?

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 ________.

At the International Pancakes Hut, there are 4 different ways to have an egg cooked, 7 different choices of pancakes, 5 different types of syrups and 8 different beverages.How many different ways are there to order an egg, a pancake with a choice of syrup and a beverage?

SCENARIO 4-1 Mothers Against Drunk Driving is a very visible group whose focus is to educate the public about the harm caused by drunk drivers.A study was recently done that emphasized the problem we all face with drinking and driving.Four 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: -Referring to Scenario 4-1, given that alcohol was not involved, what proportion of the accidents were single vehicle?

There are 47 contestants at a national dog show.How many different ways can contestants fill the first place, second place, and third place positions?

SCENARIO 4-1 Mothers Against Drunk Driving is a very visible group whose focus is to educate the public about the harm caused by drunk drivers.A study was recently done that emphasized the problem we all face with drinking and driving.Four 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: -Referring to Scenario 4-1, given that multiple vehicles were involved, what proportion of accidents involved alcohol?

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?

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