Exam 4: Basic Probability

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

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?

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

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?

True or False: If P(A or B)= 1.0, then A and B must be mutually exclusive.

The probability that a new advertising campaign will increase sales is assessed as being 0.80.The Probability that the cost of developing the new ad campaign can be kept within the original Budget allocation is 0.40.Assuming that the two events are independent, the probability that the Cost is kept within budget and the campaign will increase sales 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 4-3 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 or prefers hamburger is __________.

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

If two equally likely events A and B are mutually exclusive, what is the probability that event A Occurs?

The collection of all possible events is called

True or False: If P(A and B)= 1, then A and B must be collectively exhaustive.

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

True or False: If either A or B must occur they are called mutually exclusive.

If two events are collectively exhaustive, 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?

An exploration team of 2 women and 3 men is to be chosen from a candidate pool of 6 women and 7 men.How many different ways can this team of 5 be formed?

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, if a company is selected at random, what is the probability that the company is small to mid-sized and did not offer stock options to their board members?

SCENARIO 4-1 Mothers Against Drunk Driving is a very visible group whose main 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, what proportion of accidents involved alcohol and a single vehicle?

SCENARIO 4-1 Mothers Against Drunk Driving is a very visible group whose main 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 multiple vehicle?