Exam 4: Basic Probability

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

Seven passengers are on a waiting list for an overbooked flight.As a result of cancellations, 3 seats become available.How many ways can those 3 available seats be filled regardless of the order?

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?

The events "rolling a single die and getting four or greater" and "rolling a single die and getting a valueless than or equal to five" are mutually exclusive.

When using the general multiplication rule, P (A and B) is equal to

A new model car from Ford Motor Company offers a keyless entry system that utilizes a four- letter code.How many different possible outcomes are there for the code?

Four freshmen are to be assigned to eleven empty rooms in a student dormitory.All the rooms are considered as homogenous so that it does not matter who is being assigned to which room.How many different ways can those 4 freshmen be assigned?

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 do not own 2 cars is:

The collection of all possible events is called

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 is improperly sealed, the probability that it came from machine A is _.

SCENARIO 4-7 The next state lottery will have the following payoffs possible with their associated probabilities. Pavoff Probability \ 2.00 0.0500 \ 25.00 0.0100 \ 100.00 0.0050 \ 500.00 0.0010 \ 5,000.00 0.0005 \ 10,000.00 0.0001 You buy a single ticket. -Referring to Scenario 4-7, if you have a winning ticket, the probability that you win at least$100.00 is .

Suppose A and B are mutually exclusive events where P(A) = 0.4 and P(B) = 0.5.Then P (A andB) = .

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?

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 randomly selected company offered stock options to their board members, what is the probability that it is a large company?

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 randomly selected company is a large company, what is the probability that it offered stock options to their board members?

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

SCENARIO 4-7 The next state lottery will have the following payoffs possible with their associated probabilities. Pavoff Probability \ 2.00 0.0500 \ 25.00 0.0100 \ 100.00 0.0050 \ 500.00 0.0010 \ 5,000.00 0.0005 \ 10,000.00 0.0001 You buy a single ticket. -Referring to Scenario 4-7, the probability that you win any money is _.

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 4-3 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, assume we know that a person prefers chicken.The probability that this individual is an adult is _.

SCENARIO 4-12 Jake woke up late in the morning on the day that he has to go to school to take an important test.He can either take the shuttle bus which is usually running late 20% of the time or ride his unreliable motorcycle which breaks down 40% of the time.He decides to toss a fair coin to make his choice. -Referring to Scenario 4-12, if Jake is late to the test, what is the probability that he rode his motorcycle?