You roll a fair dice once. a) what is the

Directions: Round all probabilities to four decimal places.
You roll a fair dice once. 
a) What is the probability of rolling a 3?
b) What is the probability of rolling a 3 or 5?
c) Explain why the probability of rolling a 3 cannot be greater than the probability of rolling a 3 or 5.
You roll a single fair die two time.

a) Find the probability of observing two even numbers.

b) Find the probability of rolling zero even numbers. 
 
Consider the experiment of tossing a fair coin three times and observing either heads or tails.

a) Construct a tree diagram of the experiment.

b) Construct the sample space for the experiment.

c) What is the probability of exactly one head? 
 
In a sample of college students, 100 live on campus, 60 live with family off campus, and 40 live in an apartment off campus.

a) What is the probability a randomly selected student lives off campus?

b) What type of probability (theoretical, empirical, or intuitive) did you use to determine your answer? 
 
Explain why suits in a deck of cards (hearts, diamonds, clubs, spades) are mutually exclusive.

In a local high school with 500 students, there are 200 females, 100 sophomores, and 50 female sophomores.

a) If we choose a student at random what is the probability we choose a female or sophomore?

b) Find the probability a randomly selected student is a male or a sophomore.
c) Find the probability a randomly selected student is a female and is not a sophomore. 
The Nielsen Apps Playbook was a survey taken in 2010 of 3691 people on the use of social networking apps. The results are shown below:
Downloaded A Social Networking App in the Last 30 Days

Find the probability that a randomly chosen person has the following characteristics:

a) Is female

b) Has downloaded a social networking app in the last 30 days

c) Is a female who has downloaded a social networking app in the last 30 days.

d) Is a female or has downloaded a social networking app in the last 30 days. 
 
Given: P(Ac) = 0.8, P(B) = 0.3,  and P(B/A) = 0.2:

a) Compute P(A and B).

b) Compute P(A or B).
Thirty percent of students at a local college take statistics. Ninety percent of the students taking statistics at the college pass the course. What is the probability that a student will take statistics and pass the course?

 

Given: A and B are independent events and P(A) = 0.5 and P(B) = 0.2. Use the definition of conditional probability on page 154 to help determine:

a) P(A and B)

b) P(A/B)

c) P(B/A)
d) P(A and B)c 
At Northern Connecticut University, 55% of the students are female. Of these, 10% are business majors. Find the following probabilities assuming sampling without replacement:

a) A randomly chosen student is a female business major.

b) If possible, find the probability that two randomly selected students are business majors. If not possible, explain why not. 
 
What is the probability of an event that is impossible?

Evaluate the expression 6! / (2!4!) without using the factorial key on a calculator. Show your steps.

In how many ways can the 25 members of a 4H club select a president, a vice- president, and a treasurer?

Suppose that you roll two six-sided die. How many of the outcomes have a sum of 7?

 
A southeast regional salesman has eight destinations that he must travel to this month: Atlanta, Raleigh, Charleston, Nashville, Jacksonville, Richmond, Mobile, and Jackson. How many different possible routes could he take?

 
How many distinct strings of letters can we make by using all the letters in the word PIZZA?

 

A sit-down restaurant has two types of appetizers: garden salad and buffalo wings. It has three entrees: Spaghetti, steak and chicken. And it offers three types of dessert: ice cream, cake and pie.
 
Draw a tree diagram to represent all the meals a customer can order at this restaurant.
 
How many different meals can a customer order at this restaurant?

 
The probability that a student chosen at random from your class is a math major is 0.27. What is the probability that a student chosen at random from your class is not a math major?
 
In how many different ways can a person choose three movies to see in a theater playing 11 movies?
 
The probability that our team will finish first in the relay race is 0.25. What are the odds of our team winning the race?

 
A scholar is choosing six books to take on vacation, from a stack of 34. How many different combinations of books are there?
 
A seven-character computer password can be any three letters of the alphabet, followed by two numerical digits, followed by two more letters. How many different passwords are possible?

A hair salon did a survey of 354 customers regarding satisfaction with service and type of customer. A walk-in customer is one who has seen no ads and not been referred. The other customers either saw a TV ad or were referred to the salon (but not both). The results follow.

Assume the sample represents the entire population of customers. Find the probability that a customer is
not satisfied

not satisfied and a walk-in

very satisfied, given referred

neutral or referred

saw add and was referred

25. A Critical Thinking Exercise
According to the American Management Association, most U.S. companies now test at least some employees and job applicants for drug use. The U.S. National Institute on Drug Abuse claims that about 15% of people in the 18-25 age bracket use illegal drugs. Allyn Clark, a 21 year-old college graduate, applied for a job at the Acton Paper Company, took a drug test, and was not offered a job. He suspected that he might have failed the drug test, even though he does not use drugs. In checking with the company’s personnel department, he found that the drug test has 99% sensitivity, which means that only 1% of drug users incorrectly test negative. Also, the test has 98% specificity, meaning that only 2% of nonusers are incorrectly identified as drug users. Allyn felt relieved by these figures because he believed that they reflected a very reliable test that usually provides good results. But is this really true?
The accompanying table shows data for Allyn and 1,999 other job applicants. Based on those results:

a) Find P(false positive); that is, find the probability of randomly selecting one of the subjects who tested positive and getting someone who does not use drugs. 

b) Find P(false negative); that is, find the probability of randomly selecting someone who tested negative and getting someone who does use drugs. 

c) Are the probabilities of these wrong results low enough so that job applicants and the Acton Paper Company need not be concerned? Explain your answers.

Directions: Round all probabilities to four decimal places.
You roll a fair dice once. 
a) What is the probability of rolling a 3?
b) What is the probability of rolling a 3 or 5?
c) Explain why the probability of rolling a 3 cannot be greater than the probability of rolling a 3 or 5.
You roll a single fair die two time.

a) Find the probability of observing two even numbers.

b) Find the probability of rolling zero even numbers. 
 
Consider the experiment of tossing a fair coin three times and observing either heads or tails.

a) Construct a tree diagram of the experiment.

b) Construct the sample space for the experiment.

c) What is the probability of exactly one head? 
 
In a sample of college students, 100 live on campus, 60 live with family off campus, and 40 live in an apartment off campus.

a) What is the probability a randomly selected student lives off campus?

b) What type of probability (theoretical, empirical, or intuitive) did you use to determine your answer? 
 
Explain why suits in a deck of cards (hearts, diamonds, clubs, spades) are mutually exclusive.

In a local high school with 500 students, there are 200 females, 100 sophomores, and 50 female sophomores.

a) If we choose a student at random what is the probability we choose a female or sophomore?

b) Find the probability a randomly selected student is a male or a sophomore.
c) Find the probability a randomly selected student is a female and is not a sophomore. 
The Nielsen Apps Playbook was a survey taken in 2010 of 3691 people on the use of social networking apps. The results are shown below:
Downloaded A Social Networking App in the Last 30 Days

Find the probability that a randomly chosen person has the following characteristics:

a) Is female

b) Has downloaded a social networking app in the last 30 days

c) Is a female who has downloaded a social networking app in the last 30 days.

d) Is a female or has downloaded a social networking app in the last 30 days. 
 
Given: P(Ac) = 0.8, P(B) = 0.3,  and P(B/A) = 0.2:

a) Compute P(A and B).

b) Compute P(A or B).
Thirty percent of students at a local college take statistics. Ninety percent of the students taking statistics at the college pass the course. What is the probability that a student will take statistics and pass the course?

 

Given: A and B are independent events and P(A) = 0.5 and P(B) = 0.2. Use the definition of conditional probability on page 154 to help determine:

a) P(A and B)

b) P(A/B)

c) P(B/A)
d) P(A and B)c 
At Northern Connecticut University, 55% of the students are female. Of these, 10% are business majors. Find the following probabilities assuming sampling without replacement:

a) A randomly chosen student is a female business major.

b) If possible, find the probability that two randomly selected students are business majors. If not possible, explain why not. 
 
What is the probability of an event that is impossible?

Evaluate the expression 6! / (2!4!) without using the factorial key on a calculator. Show your steps.

In how many ways can the 25 members of a 4H club select a president, a vice- president, and a treasurer?

Suppose that you roll two six-sided die. How many of the outcomes have a sum of 7?

 
A southeast regional salesman has eight destinations that he must travel to this month: Atlanta, Raleigh, Charleston, Nashville, Jacksonville, Richmond, Mobile, and Jackson. How many different possible routes could he take?

 
How many distinct strings of letters can we make by using all the letters in the word PIZZA?

 

A sit-down restaurant has two types of appetizers: garden salad and buffalo wings. It has three entrees: Spaghetti, steak and chicken. And it offers three types of dessert: ice cream, cake and pie.
 
Draw a tree diagram to represent all the meals a customer can order at this restaurant.
 
How many different meals can a customer order at this restaurant?

 
The probability that a student chosen at random from your class is a math major is 0.27. What is the probability that a student chosen at random from your class is not a math major?
 
In how many different ways can a person choose three movies to see in a theater playing 11 movies?
 
The probability that our team will finish first in the relay race is 0.25. What are the odds of our team winning the race?

 
A scholar is choosing six books to take on vacation, from a stack of 34. How many different combinations of books are there?
 
A seven-character computer password can be any three letters of the alphabet, followed by two numerical digits, followed by two more letters. How many different passwords are possible?

A hair salon did a survey of 354 customers regarding satisfaction with service and type of customer. A walk-in customer is one who has seen no ads and not been referred. The other customers either saw a TV ad or were referred to the salon (but not both). The results follow.

Assume the sample represents the entire population of customers. Find the probability that a customer is
not satisfied

not satisfied and a walk-in

very satisfied, given referred

neutral or referred

saw add and was referred

25. A Critical Thinking Exercise
According to the American Management Association, most U.S. companies now test at least some employees and job applicants for drug use. The U.S. National Institute on Drug Abuse claims that about 15% of people in the 18-25 age bracket use illegal drugs. Allyn Clark, a 21 year-old college graduate, applied for a job at the Acton Paper Company, took a drug test, and was not offered a job. He suspected that he might have failed the drug test, even though he does not use drugs. In checking with the company’s personnel department, he found that the drug test has 99% sensitivity, which means that only 1% of drug users incorrectly test negative. Also, the test has 98% specificity, meaning that only 2% of nonusers are incorrectly identified as drug users. Allyn felt relieved by these figures because he believed that they reflected a very reliable test that usually provides good results. But is this really true?
The accompanying table shows data for Allyn and 1,999 other job applicants. Based on those results:

a) Find P(false positive); that is, find the probability of randomly selecting one of the subjects who tested positive and getting someone who does not use drugs. 

b) Find P(false negative); that is, find the probability of randomly selecting someone who tested negative and getting someone who does use drugs. 

c) Are the probabilities of these wrong results low enough so that job applicants and the Acton Paper Company need not be concerned? Explain your answers.