Exam 4: Basic Probability

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 ethical practice to explain to the clienteles what the basis of her probability estimate 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?

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?

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. Did Well on Midterm Did Poorly on Midterm Studying for Exam 80 20 Went Bar Hopping 30 70 -Referring to Scenario 4-2, the events "Did Well on Midterm" and "Studying for Exam" are

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. Did Well on Midterm Did Poorly on Midterm Studying for Exam 80 20 Went Bar Hopping 30 70 -Referring to Scenario 4-2, the events "Did Well on Midterm" and "Studying for Exam" are

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.

SCENARIO 4-10 Are whites more likely to claim bias? It was found that 60% of the workers were white, 30% were black and 10% are other races.Given that a worker was white, the probability that the worker had claimed bias was 30%.Given that a worker was black, the probability that the worker had claimed bias was 40%.Given that a worker was other race, the probability that the worker had claimed bias was 0%. -Referring to Scenario 4-10, if a randomly selected worker had not claimed bias, what is the probability that the worker is white?

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 the person is a child.The probability that this individual prefers hamburger is .

Simple probability is also called

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 of a household do not own 2 cars and have an income over $50,000 a year is:

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

If either event A or event B must occur, then events A and B are said to be

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

When A and B are mutually exclusive, P (A or B) can be found by adding P(A) andP(B).

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 not include any of the twin brothers?

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 southern Texas, the probability the student has not passed the ELM is .

The closing price of a company's stock tomorrow can be lower, higher or the same as today's closed.Without any prior information that may affect the price of the stock tomorrow, the probability that it will close higher than today's close is 1/3.This is an example of using which of the following probability approach?

SCENARIO 4-10 Are whites more likely to claim bias? It was found that 60% of the workers were white, 30% were black and 10% are other races.Given that a worker was white, the probability that the worker had claimed bias was 30%.Given that a worker was black, the probability that the worker had claimed bias was 40%.Given that a worker was other race, the probability that the worker had claimed bias was 0%. -Referring to Scenario 4-10, when a randomly selected worker was not white, what is the probability that the worker had not claimed bias?

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

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 took the bus?