BUSI 230 HW 5.1, HW 5.2, HW 5.3, HW 5.4 Connect Exercises Week 3 solutions complete answers

BUSI 230 HW 5.1, HW 5.2, HW 5.3, HW 5.4 Connect Exercises Week 3 solutions complete answers 

HW 5.1 Basic Concepts of Probability Assignment 

 

Fill in the blank with the appropriate word or phrase.

If an event cannot occur, its probability is .

If an event is certain to occur, its probability is .

The collection of all possible outcomes of a probability experiment is called .

An outcome or collection of outcomes from a sample space is called .

 

Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6}, and all the outcomes are equally likely. Find P(2). Express your answer in exact form.

Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6}, and all the outcomes are equally likely. Find P(0). Express your answer in exact form.

Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6}, and all the outcomes are equally likely. Find P(7). Express your answer in exact form.

Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6}, and all the outcomes are equally likely. Find P(Odd number). Express your answer in exact form.

 

Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6}, and all the outcomes are equally likely. Find P(less than 5). Write your answer as a fraction or whole number.

Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6}, and all the outcomes are equally likely. Find P(greater than 0). Write your answer as a fraction or whole number.

Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6}, and all the outcomes are equally likely. Find P(greater than 1). Write your answer as a fraction or whole number.

Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6}, and all the outcomes are equally likely. Find P(greater than 2). Write your answer as a fraction or whole number.

Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6}, and all the outcomes are equally likely. Find P(greater than 3). Write your answer as a fraction or whole number.

Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6}, and all the outcomes are equally likely. Find P(greater than 4). Write your answer as a fraction or whole number.

Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6}, and all the outcomes are equally likely. Find P(greater than 5). Write your answer as a fraction or whole number.

Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6}, and all the outcomes are equally likely. Find P(greater than 7). Write your answer as a fraction or whole number.

 

Assume that a coin is tossed twice. The coin may not be fair. The sample space consists of the outcomes {HH, HT, TH, TT}.

 

How probable is it? Someone computes the probabilities of several events. The probabilities are listed below. Select the best verbal description for each probability.

 

Who will you vote for? In a survey of 500 likely voters in a certain city, 290 said that they planned to vote to reelect the incumbent mayor.

(a) What is the probability that a surveyed voter plans to vote to reelect the mayor? Express your answer as a decimal rounded to two decimal places.

The probability that a surveyed voter plans to vote to reelect the mayor is

(b) Interpret this probability by estimating the percentage of all voters in the city who plan to vote to reelect the mayor.

The estimated percentage of all voters in the city who plan to vote to reelect the mayor is

 

True–false exam: A section of an exam contains four true–false questions. A completed exam paper is selected at random, and the four answers are recorded. Round your answers to four decimal places if necessary.

Assuming the outcomes to be equally likely, find the probability that all the answers are "False."

The probablility that all the answers are "False" is

Assuming the outcomes to be equally likely, find the probability that exactly three of the four answers is "True."

Assuming the outcomes to be equally likely, find the probability that two of the answers are "True" and two of the answers are "False."

Assuming the outcomes to be equally likely, find the probability that all the answers are the same.

Assuming the outcomes to be equally likely, find the probability that exactly three of the four answers is "False."

Assuming the outcomes to be equally likely, find the probability that the first answer is "False."

Assuming the outcomes to be equally likely, find the probability that exactly one of the four answers is "True."

Assuming the outcomes to be equally likely, find the probability that the last answer is "False."

Assuming the outcomes to be equally likely, find the probability that exactly one of the four answers is "False."

Assuming the outcomes to be equally likely, find the probability that all the answers are "True."

 

Empirical Method: A die is rolled 300 times. On 25 of those rolls, the die comes up 5. Use the Empirical method to approximate the probability that the die comes up 5. Round your answer to four decimal places as necessary.

The probability that the die comes up  is approximately .

 

More pitching: A baseball pitcher threw 3148 pitches during part of a recent season. Of these, 1611 were thrown with no strikes on the batter, 976 were thrown with one strike, and 561 were thrown with two strikes.

(a) What is the probability that a baseball pitch is thrown with no strikes? Round your answer to four decimal places.

(b) What is the probability that a baseball pitch is thrown with fewer than two strikes? Round your answer to four decimal places.

 

Get an education: A survey asked 32,180 people how much confidence they had in educational institutions. The results were as follows. Round your answers to four decimal places if necessary.

(a) What is the probability that a sampled person has either some or hardly any confidence in educational institutions?

The probability that a sampled person has either some or hardly any confidence in educational institutions is

(b) Assume this is a simple random sample from a population. Use the Empirical Method to estimate the probability that a person has hardly any confidence in educational institutions.

(c) If we use a cutoff of 0.05, is it unusual for someone to have some confidence in educational institutions?

(a) What is the probability that a sampled person has either a great deal or some confidence in educational institutions?

(b) Assume this is a simple random sample from a population. Use the Empirical Method to estimate the probability that a person has a great deal of confidence in educational institutions.

(c) If we use a cutoff of 0.05, is it unusual for someone to have a great deal of confidence in educational institutions?

(a) What is the probability that a sampled person has either a great deal or hardly any confidence in educational institutions?

(b) Assume this is a simple random sample from a population. Use the Empirical Method to estimate the probability that a person has some confidence in educational institutions.

(c) If we use a cutoff of 0.05, is it unusual for someone to have a great deal of confidence in educational institutions?

 

Liberty University BUSI 230 HW 5.2 The Addition Rule and the Rule of Complements Assignment complete solutions answers and more!

 

The General Addition Rule states that .

If events A and B are mutually exclusive, then .

Given an event A, the event that A does not occur is called the  of .

The Rule of Complements states that .

 

If P(A)=0.46, P(B)=0.7, and P(A and B)=0.4, find P(A or B).

 

If P(A)=0.6, P(B)=0.3, and A and B are mutually exclusive, find P(A or B).

 

If P(A)=0.46, P(B)=0.7, and P(A or B)=0.4 are A and B mutually exclusive?

 

If P(B)=0.2, find P(B^c).

 

Determine whether events A and B are mutually exclusive.

 

A red die and a blue die are rolled.

A: The red die comes up 5.

B: The total is 4.

 

A: Jayden has a math class on Tuesdays at 2:00

B: Jayden has an English class on Wednesdays at 2:00

 

A sample of 300 phone batteries was selected. Find the complements of the following events.

(a)More than 233 of the batteries were defective.

(b)At least 233 of the batteries were defective.

(c)Fewer than 233 of the batteries were defective.

(d)Exactly 233 of the batteries were defective.

 

Car repairs: Let E be the event that a new car requires engine work under warranty and let T be the event that the car requires transmission work under warranty. Suppose that P(E)=0.1, P(T)=0.09, P(E and T)=0.02.

(a) Find the probability that the car needs work on either the engine, the transmission, or both.

(b) Find the probability that the car needs no work on the engine.

(b) Find the probability that the car needs no work on the transmission.

 

Computer purchases: Out of 812 large purchases made at a computer retailer, 349 were personal computers, 396 were laptop computers, and 67 were printers. As a part of an audit, one purchase record is sampled at random. Round the answers to four decimal places, as needed.

(a) What is the probability that it is a tablet?

(b) What is the probability that it is not a laptop computer?

 

Visit your local library: On a recent Saturday, a total of 1351 people visited a local library. Of these people, 254 were under age 10, 165 were aged 10-18, 152 were aged 19-30, and the rest were more than 30 years old. One person is sampled at random.

 

(a) What is the probability that the person is less than 19 years old? Round your answer to four decimal places.

(b) What is the probability that the person is more than 18 years old? Round your answer to four decimal places.

 

Weight and cholesterol: The National Health Examination Survey reported that in a sample of 13136 adults, 6305 had high cholesterol (total cholesterol above  200 mg/dL), 8407 were overweight (body mass index above 25), and 3941 were both overweight and had high cholesterol. A person is chosen at random from this study. Round all answers to four decimal places.

(a)Find the probability that the person is overweight.

The probability that the person is overweight is .

(b)Find the probability that the person has high cholesterol.

The probability that the person has high cholesterol is .

(c)Find the probability that the person does not have high cholesterol.

The probability that the person does not have high cholesterol is .

(d)Find the probability that the person is overweight or has high cholesterol.

The probability that the person is overweight or has high cholesterol is .

 

Liberty University BUSI 230 HW 5.3 Conditional Probability and the Multiplication Rule Assignment complete solutions answers and more!

 

Fill in each blank with the appropriate word or phrase.

A probability that is computed with the knowledge of additional information is called .

 

The General Multiplication Rule states that .

 

Two events are  if the occurrence of one does not affect the probability that the other event occurs.

 

Let A and B be events with P(A)=0.2, P(B)=0.98, and P(B/A)=0.1. Find P(A and B).

 

Let A and B be events with P(A)=0.2, P(B)=0.7. Assume that A and B are independent. Find P(A and B).

 

A fair coin is tossed five times. What is the probability that the sequence of tosses is HTHTH? Write your answer as a fraction or a decimal, rounded to four decimal places.

The probability that the sequence of tosses is HTHT is

 

Assume that a student is chosen at random from a class. Determine whether the events A and B are independent, mutually exclusive, or neither.

A: The student is a woman.

B: The student belongs to a sorority.

 

Let A and B be events with P(A)=0.3, P(B)=0.2, and P(A or B)=0.18.

(a) Are A and B independent? Explain.

(b) Compute P(A and B).

(c) Are A and B mutually exclusive? Explain.

 

An unfair coin has probability 0.4 of landing heads. The coin is tossed seven times. What is the probability that it lands heads at least once? Round the answer to four decimal places.

P(Lands heads at least once)=

 

Shuffle: Charles has three songs on a playlist. Each song is by a different artist. The artists are Drake, Ed Sheeran, and BTS. He programs his player to play the songs in a random order, without repetition. What is the probability that the first song is by Ed Sheeran and the second song is by Drake? Write your answer as a fraction or a decimal, rounded to four decimal places.

The probability that the first song is by Ed Sheeran and the second song is by Drake is

 

Let's eat: A fast-food restaurant chain has 591 outlets in the United States. The following table categorizes them by city population size and location, and presents the number of restaurants in each category. A restaurant is to be chosen at random from the 591 to test market a new menu. Round your answers to four decimal places.

(a) Given that the restaurant is located in a city with a population over 500,000, what is the probability that it is in the Northeast?

(b) Given that the restaurant is located in the Southeast, what is the probability that it is in a city with a population under 50,000?

(c) Given that the restaurant is located in the Southwest, what is the probability that it is in a city with a population of 500,000 or less?

(d) Given that the restaurant is located in a city with a population of 500,000 or less, what is the probability that it is in the Southwest?

(e) Given that the restaurant is located in the South (either SE or SW), what is the probability that it is in a city with a population of 50,000 or more?

 

Genetics: A geneticist is studying two genes. Each gene can be either dominant or recessive. A sample of 100 individuals is categorized as follows. Write your answer as a fraction or a decimal, rounded to four decimal places.

(a) What is the probability that in a randomly sampled individual, gene 1 is recessive?

(b) What is the probability that in a randomly sampled individual, gene 2 is recessive?

(c) Given that gene 1 is recessive, what is the probability that gene 2 is recessive?

(d) Two genes are said to be in linkage equilibrium if the event that gene 1 is recessive is independent of the event that gene 2 is recessive. Are these genes in linkage equilibrium?

(a) What is the probability that in a randomly sampled individual, gene 1 is dominant?

 

Stay in school: In a recent school year in the state of Washington, there were 324,000 high school students. Of these, 157,000 were girls and 167,000 were boys. Among the girls, 70,700 dropped out of school, and among the boys, 10,300 dropped out. A student is chosen at random. Round the answers to four decimal places.

(a) What is the probability that the student is male?

(b) What is the probability that the student dropped out?

(c) What is the probability that the student is male and dropped out?

(d) Given that the student is male, what is the probability that he dropped out?

(e) Given that the student dropped out, what is the probability that the student is male?

(a) What is the probability that the student is female?

 

GED: In a certain high school, the probability that a student drops out is 0.03, and the probability that a dropout gets a high-school equivalency diploma (GED) is 0.31. What is the probability that a randomly selected student gets a GED? Round your answer to four decimal places, if necessary.

The probability that the randomly selected student gets a GED is

 

Defective components: A lot of 9 components contains 4 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. Write your answer as a fraction or a decimal, rounded to four decimal places.

Are A dn B independent? Explain.

 

Lottery: Every day, Jorge buys a lottery ticket. Each ticket has a probability of 0.4 of winning a prize. After sex days, what is the probability that Jorge has won at least one prize? Round your answer to four decimal places.

The probability that Jorge has won at least one prize is

 

Liberty University BUSI 230 HW 5.4 Counting Assignment complete solutions answers and more!

 

Evaluate the expression.

 

Evaluate the permutation.

 

Evaluate the combination.

 

Pizza time: A local pizza parlor is offering a half-price deal on any pizza with one topping. There are six toppings from which to choose. In addition, there are four different choices for the size of the pizza, and three choices for the type of crust. In how many ways can a pizza be ordered?

 

License plates: In a certain state, license plates consist of five digits from 0 to 9 followed by three letters. Assume the numbers and letters are chosen at random. Replicates are allowed.

(a) How many different license plates can be formed?

(b) How many different license plates have the letters J-O in that order?

(c) If your name is Jo, what is the probability that your name is on your license plate?

(c) If your name is Jo, what is the probability that your name is on your license plate? Write your answer as a fraction or a decimal, rounded to at least 5 places.

(b) How many different license plates have the letters T-O-M in that order?

(b) How many different license plates have the letters K-E-M-P in that order?

 

Committee: The Student Council at a certain school has ten members. Four members will form an executive committee consisting of a president, a vice president, a secretary, and a treasurer.

In how many ways can these four positions be filled?

In how many ways can four people be chosen for the executive committee if it does not matter who gets which position?

Four of the people on Student Council are Zachary, Yolanda, Xavier, and Walter. What is the probability that Zachary is president, Yolanda is vice president, Xavier is secretary, and Walter is treasurer? Round your answers to at least 6 decimal places.

What is the probability that Zachary, Yolanda, Xavier, and Walter are the four committee members? Round your answers to at least  decimal places.