BackIndependent?
Refer to the contingency table in Problem 17 that relates age and likelihood to buy American. Determine P(45–54 years old) and P(45–54 years old | more likely). Are the events "45–54 years old" and "more likely" independent?
Party Affiliation
The following data represent political party by age from a random sample of registered Iowa voters.
b. Are the events "Democrat" and "65+" independent? Justify your answer.
Alarm Clock Life Hack Each of us must sometimes wake up early for something really important, such as a final exam, job interview, or an early flight. (Professional golfer Jim Furyk was disqualified from a tournament when his cellphone lost power and he overslept.) Assume that a battery-powered alarm clock has a 0.005 probability of failure, a smartphone alarm clock has a 0.052 probability of failure, and an electric alarm clock has a 0.001 probability of failure.
a. What is the probability that your single battery-powered alarm clock works successfully when you need it?
Marriage and Education
According to the U.S. Census Bureau, 20.2% of American women aged 25 years or older have a Bachelor's Degree. 16.5% have never married. Among women 25 years or older who have never married, 22.8% have a Bachelor's Degree. Among women 25 years or older who have a Bachelor's Degree, 18.6% have never married.
a. Are the events "have a Bachelor's Degree" and "never married" independent? Explain.
Alarm Clock Life Hack Each of us must sometimes wake up early for something really important, such as a final exam, job interview, or an early flight. (Professional golfer Jim Furyk was disqualified from a tournament when his cellphone lost power and he overslept.) Assume that a battery-powered alarm clock has a 0.005 probability of failure, a smartphone alarm clock has a 0.052 probability of failure, and an electric alarm clock has a 0.001 probability of failure.
b. If you use a battery-powered alarm clock and a smartphone alarm clock, what is the probability that they both fail? What is the probability that both of them do not fail?
Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.
25. Best President In a sample of 1500 adult U.S. citizens, 270 said that Barack Obama was the best president in U.S. history. Two adult U.S. citizens are selected at random.
(Adapted from YouGov)
d. Which of the events can be considered unusual? Explain.
Double Jackpot Shawn lives near the border of Illinois and Missouri. One weekend he decides to play \$1 in both state lotteries in hopes of hitting two jackpots. The probability of winning the Missouri Lotto is about 0.00000028357 and the probability of winning the Illinois Lotto is about 0.000000098239.
b. Find the probability that Shawn will win both jackpots.
Same Birthdays If 25 people are randomly selected, find the probability that no 2 of them have the same birthday. Ignore leap years.
"Blood TypesA person can have one of four blood types: A, B, AB, or O.
If a person is randomly selected, is the probability they have blood type A equal to 1/4? Why or why not?"
Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.
24. Knowing a Person Who Was Murdered In a sample of 11,771 children ages 2 to 17, 8% have lost a friend or relative to murder. Four children are selected at random. (Adapted from University of New Hampshire)
a. Find the probability that all four have lost a friend or relative to murder.
Earn More Than Your Parents?
In 1970, 92% of American 30-year-olds earned more than their parents did at age 30 (adjusted for inflation). In 2014, only 51% of American 30-year-olds earned more than their parents did at age 30. Source: Wall Street Journal, December 8, 2016.
b. What is the probability that two randomly selected 30-year-olds in 1970 earned more than their parents at age 30?
During the 2018 season, the Chicago Cubs won 58% of their games. Assuming game outcomes are independent and the win percentage remains the same for this season, answer the following:
b. What is the probability that the Cubs will win seven consecutive games?
Reliability
For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.15 probability of failure.
c. How many components would be needed in the structure so that the probability the system will succeed is greater than 0.999999?
Police Complaints The Chicago Tribune analyzed 17,713 complaints by citizens against Chicago police officers.
d. Of the 794 complaints with an affidavit that were found to be legitimate, 12 resulted in the officer being dismissed. Is it unusual for a legitimate complaint with an affidavit to result in the officer being dismissed?
Manufacturing An assembly line produces 10,000 automobile parts. Twenty percent of the parts are defective. An inspector randomly selects 10 of the parts
b. Because the sample is only 0.1% of the population, treat the events as independent and use the binomial probability formula to approximate the probability that none of the selected parts are defective.