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intro stats

Intro Stats 4th International Edition Richard D. De Veaux, Paul F. Velleman, David Bock - Solutions

Batteries A junk box in your room contains a dozen old batteries, five of which are totally dead. You start picking batteries one at a time and testing them. Find the probability of each outcome.a) The first two you choose are both good.b) At least one of the first three works.c) The first four you
Another hand You pick three cards at random from a deck. Find the probability of each event described below.a) You get no aces.b) You get all hearts.c) The third card is your first red card.d) You have at least one diamond.
Cards You are dealt a hand of three cards, one at a time.Find the probability of each of the following.a) The first heart you get is the third card dealt.b) Your cards are all red (that is, all diamonds or hearts).c) You get no spades.d) You have at least one ace.
Sick cars Twenty percent of cars that are inspected have faulty pollution control systems. The cost of repairing a pollution control system exceeds $100 about 40% of the time. When a driver takes her car in for inspection, what’s the probability that she will end up paying more than $100 to
Sick kids Seventy percent of kids who visit a doctor have a fever, and 30% of kids with a fever also have sore throats. What’s the probability that a kid who goes to the doctor has a fever and a sore throat?
Birth order, take 2 Look again at the data about birth order of Intro Stats students and their choices of colleges shown in Exercise 20.a) If we select a student at random, what’s the probability the person is an Arts and Sciences student who is a second child (or more)?b) Among the Arts and
Global survey, take 2 Look again at the table summarizing the Roper survey in Exercise 19.a) If we select a respondent at random, what’s the probability we choose a person from the United States who has done post-graduate study?b) Among the respondents who have done post-graduate study, what’s
Immigration The table shows the political affiliations of U.S. voters and their positions on supporting stronger immigration enforcement.a) What’s the probability that i) a randomly chosen voter favors stronger immigration enforcement?ii) a Republican favors stronger enforcement?iii) a voter who
Health The probabilities that an adult American man has high blood pressure and/or high cholesterol are shown in the table.What’s the probability thata) a man has both conditions?b) a man has high blood pressure?c) a man with high blood pressure has high cholesterol?d) a man has high blood
Pets In its monthly report, the local animal shelter states that it currently has 24 dogs and 18 cats available for adoption. Eight of the dogs and 6 of the cats are male.Find each of the following conditional probabilities if an animal is selected at random:a) The pet is male, given that it is a
Cards You draw a card at random from a standard deck of 52 cards. Find each of the following conditional probabilities:a) The card is a heart, given that it is red.b) The card is red, given that it is a heart.c) The card is an ace, given that it is red.d) The card is a queen, given that it is a
Birth order A survey of students in a large Introductory Statistics class asked about their birth order(1 = oldest or only child) and which college of the university they were enrolled in. Here are the data:Suppose we select a student at random from this class.What is the probability that the
Global survey The marketing research organization GfK Roper conducts a yearly survey on consumer attitudes worldwide. They collect demographic information on the roughly 1500 respondents from each country that they survey. Here is a table showing the number of people with various levels of
Workers Employment data at a large company reveal that 72% of the workers are married, that 44% are college graduates, and that half of the college grads are married.What’s the probability that a randomly chosen workera) is neither married nor a college graduate?b) is married but not a college
Amenities A check of dorm rooms on a large college campus revealed that 38% had refrigerators, 52% had TVs, and 21% had both a TV and a refrigerator. What’s the probability that a randomly selected dorm room hasa) a TV but no refrigerator?b) a TV or a refrigerator, but not both?c) neither a TV
Travel Suppose the probability that a U.S. resident has traveled to Canada is 0.18, to Mexico is 0.09, and to both countries is 0.04. What’s the probability that an American chosen at random hasa) traveled to Canada but not Mexico?b) traveled to either Canada or Mexico?c) not traveled to either
Phones Recent research suggests that 73% of Americans have a home phone, 83% have a cell phone, and 58% of people have both. What is the probability that an American hasa) a home or cell phone?b) neither a home phone nor a cell phone?c) a cell phone but no home phone?
Of those younger than 50, 5 of 8 conduct their banking online. Of those older than 50, only 1 of 12 banks online. Draw a tree for this situation. Why is the tree better than the table in this case? Where are the joint probabilities found?
Online banking again Suppose that the information in Exercise 10 had been presented in the following way.A national survey of bank customers finds that 40% are younger than
Facebook again Suppose that the information in Exercise 9 had been presented in the following way. Facebook reports that 70% of its users are from outside the United States.Of the U.S. users, two-thirds log on every day. Of the non-U.S. users, three-sevenths log on every day. Draw a tree for this
Online banking A national survey indicated that 30% of adults conduct their banking online. It also found that 40%are younger than 50, and that 25% are younger than 50 and conduct their banking online. Make a probability table. Why is a table better than a tree here?
Facebook Facebook reports that 70% of its users are from outside the United States and that 50% of its users log on to Facebook every day. Suppose that 20% of its users are U.S. users who log on every day. Make a probability table. Why is a table better than a tree here?
Births If the sex of a child is independent of all other births, is the probability of a woman giving birth to a girl after having four boys greater than it was on her first birth? Explain.
Titanic On the Titanic, the probability of survival was 0.323. Among first class passengers, it was 0.625. Were survival and ticket class independent? Explain.
Field goals A nervous kicker usually makes 70% of his first field goal attempts. If he makes his first attempt, his success rate rises to 90%. What is the probability that he makes his first two kicks?
Late to the train A student figures that he has a 30%chance of being let out of class late. If he leaves class late, there is a 45% chance that he will miss his train. What is the probability that he misses the train?
Sports again From Exercise 3, if someone doesn’t like to watch basketball, what is the probability that she will be a football fan?
Sports What is the probability that a person likes to watch football, given that she also likes to watch basketball?Football No Football Basketball 27 13 No Basketball 38 22
Cooking and shopping Forty-five percent of Americans like to cook and 59% of Americans like to shop, while 23% enjoy both activities. What is the probability that a randomly selected American either enjoys cooking or shopping or both?
Pet ownership Suppose that 25% of people have a dog, 29% of people have a cat, and 12% of people own both.What is the probability that someone owns a dog or a cat?
Red cards You shuffle a deck of cards and then start turning them over one at a time. The first one is red. So is the second. And the third. In fact, you are surprised to get 10 red cards in a row. You start thinking, “The next one is due to be black!”a) Are you correct in thinking that
9/11? On September 11, 2002, the first anniversary of the terrorist attack on the World Trade Center, the New York State Lottery’s daily number came up 9–1–1. An interesting coincidence or a cosmic sign?a) What is the probability that the winning three numbers match the date on any given
Pepsi For a sales promotion, the manufacturer places winning symbols under the caps of 10% of all Pepsi bottles. You buy a six-pack. What is the probability that you win something?
Lights You purchased a five-pack of new light bulbs that were recalled because 6% of the lights did not work. What is the probability that at least one of your lights is defective?
Religion Census reports for a city indicate that 62%of residents classify themselves as Christian, 12%as Jewish, and 16% as members of other religions( Muslims, Buddhists, etc.). The remaining residents classify themselves as nonreligious. A polling organization seeking information about public
Voters Suppose that in your city 37% of the voters are registered as Democrats, 29% as Republicans, and 11%as members of other parties (Liberal, Right to Life, Green, etc.). Voters not aligned with any official party are termed “Independent.” You are conducting a poll by calling registered
The train To get to work, a commuter must cross train tracks. The time the train arrives varies slightly from day to day, but the commuter estimates he’ll get stopped on about 15% of work days. During a certain 5-day work week, what is the probability that hea) gets stopped on Monday and again on
Champion bowler A certain bowler can bowl a strike 70% of the time. If the bowls are independent, what’s the probability that shea) goes three consecutive frames without a strike?b) makes her first strike in the third frame?c) has at least one strike in the first three frames?d) bowls a perfect
Slot machine A slot machine has three wheels that spin independently. Each has 10 equally likely symbols:4 bars, 3 lemons, 2 cherries, and a bell. If you play, what is the probability thata) you get 3 lemons?b) you get no fruit symbols?c) you get 3 bells (the jackpot)?d) you get no bells?e) you get
Dice You roll a fair die three times. What is the probability thata) you roll all 6’s?b) you roll all odd numbers?c) none of your rolls gets a number divisible by 3?d) you roll at least one 5?e) the numbers you roll are not all 5’s?
Disjoint or independent? In Exercise 40, you calculated probabilities involving various blood types. Some of your answers depended on the assumption that the outcomes described were disjoint; that is, they could not both happen at the same time. Other answers depended on the assumption that the
Disjoint or independent? In Exercise 39, you calculated probabilities of getting various M&M’s. Some of your answers depended on the assumption that the outcomes described were disjoint; that is, they could not both happen at the same time. Other answers depended on the assumption that the events
at least one person is Type B?
they are not all Type A?
no one is Type AB?
all are Type O?
is not Type O?b) Among four potential donors, what is the probability that
has Type A or Type B?
has Type AB blood?
Blood The American Red Cross says that about 45%of the U.S. population has Type O blood, 40% Type A, 11% Type B, and the rest Type AB.a) Someone volunteers to give blood. What is the probability that this donor
at least one is green?
none are yellow?
the third one is the first one that’s red?
they are all brown?
it is striped?b) If you pick three M&M’s in a row, what is the probability that
it is not green?
it is yellow or orange?
it is brown?
M&M’s The Mars company says that before the introduction of purple, yellow candies made up 20% of their plain M&M’s, red another 20%, and orange, blue, and green each made up 10%. The rest were brown.a) If you pick an M&M at random, what is the probability that
Polling, part II According to Pew Research, the contact rate (probability of contacting a selected household) was 69% in 1997 and 76% in 2003. However, the cooperation rate (probability of someone at the contacted household agreeing to be interviewed) was 58% in 1997 and dropped to 38% in 2003.a)
Polling As mentioned in the chapter, opinion-polling organizations contact their respondents by sampling random telephone numbers. Although interviewers can reach about 76% of U.S. households, the percentage of those contacted who agree to cooperate with the survey fell from 58% in 1997 to only 38%
If we select two people at random from this sample,a) what is the probability that both think that being a father is easier today?b) what is the probability that neither thinks being a father is easier today?c) what is the probability that the first person thinks being a father is easier today and
Fathers, revisited Consider again the results of the poll about fathering discussed in Exercise
More energy Exercise 33 shows the results of a Gallup Poll about energy. Suppose we select three people at random from this sample.a) What is the probability that all three responded “Protect the environment”?b) What is the probability that none responded “Equally important”?c) What
Failing fathers? A Pew Research poll in 2011 asked 2005 U.S. adults whether being a father today is harder than it was a generation ago. Here’s how they responded:If we select a respondent at random from this sample of 2005 adults,a) what is the probability that the selected person responded
Energy 2011 A Gallup Poll in March 2011 asked 1012 U.S. adults whether increasing domestic energy production or protecting the environment should be given a higher priority. Here are the results:If we select a person at random from this sample of 1012 adults,a) what is the probability that the
Final project You used the Multiplication Rule to calculate probabilities about the Calculus background of your Statistics groupmates in Exercise 30.a) What must be true about the groups in order to make that approach valid?b) Do you think this assumption is reasonable? Explain.
Repairs again You used the Multiplication Rule to calculate repair probabilities for your cars in Exercise 29.a) What must be true about your cars in order to make that approach valid?b) Do you think this assumption is reasonable? Explain.
What is the probability that of your other two groupmates,a) neither has studied Calculus?b) both have studied at least one semester of Calculus?c) at least one has had more than one semester of Calculus?
Another project You are assigned to be part of a group of three students from the Intro Stats class described in Exercise
If you own two cars, what is the probability thata) neither will need repair?b) both will need repair?c) at least one car will need repair?
More repairs Consider again the auto repair rates described in Exercise
Energy 2011 A Gallup Poll in March 2011 asked 1012 U.S. adults whether increasing domestic energy production or protecting the environment should be given a higher priority. Here are the results:
Final project You used the Multiplication Rule to calculate probabilities about the Calculus background of your Statistics groupmates in Exercise 30.a) What must be true about the groups in order to make that approach valid?b) Do you think this assumption is reasonable? Explain.
Repairs again You used the Multiplication Rule to calculate repair probabilities for your cars in Exercise 29.a) What must be true about your cars in order to make that approach valid?b) Do you think this assumption is reasonable? Explain.
What is the probability that of your other two groupmates,a) neither has studied Calculus?b) both have studied at least one semester of Calculus?c) at least one has had more than one semester of Calculus?
Another project You are assigned to be part of a group of three students from the Intro Stats class described in Exercise
If you own two cars, what is the probability thata) neither will need repair?b) both will need repair?c) at least one car will need repair?
More repairs Consider again the auto repair rates described in Exercise
Stats projects In a large Introductory Statistics lecture hall, the professor reports that 55% of the students enrolled have never taken a Calculus course, 32% have taken only one semester of Calculus, and the rest have taken two or more semesters of Calculus. The professor randomly assigns
Car repairs A consumer organization estimates that over a 1-year period 17% of cars will need to be repaired only once, 7% will need repairs exactly twice, and 4% will require three or more repairs. What is the probability that a car chosen at random will needa) no repairs?b) no more than one
College admissions II In Exercise 25, we saw that in 2007 Harvard accepted about 7% of its applicants, MIT 10%, and Penn 14%. Jorge has applied to all three. He figures that his chances of getting into at least one of the three must be about 31%.a) How has he arrived at this conclusion?b) What
College admissions For high school students graduating in 2007, college admissions to the nation’s most selective schools were the most competitive in memory (Source: The New York Times, “A Great Year for Ivy League Schools, but Not So Good for Applicants to Them,” April 4, 2007).Harvard
Lefties Although it’s hard to be definitive in classifying people as right- or left-handed, some studies suggest that about 14% of people are left-handed. Since 0.14 * 0.14 = 0.0196, the Multiplication Rule might suggest that there’s about a 2% chance that a brother and a sister are both
Speeders Traffic checks on a certain section of highway suggest that 60% of drivers are speeding there. Since 0.6 * 0.6 = 0.36, the Multiplication Rule might suggest that there’s a 36% chance that two vehicles in a row are both speeding. What’s wrong with that reasoning?
Homes Funding for many schools comes from taxes based on assessed values of local properties. People’s homes are assessed higher if they have extra features such as garages and swimming pools. Assessment records in a certain school district indicate that 37% of the homes have garages and 3% have
Electronics Suppose that 46% of families living in a certain county own a computer and 18% own an HDTV. The Addition Rule might suggest, then, that 64% of families own either a computer or an HDTV. What’s wrong with that reasoning?
Scratch off Many stores run “secret sales”: Shoppers receive cards that determine how large a discount they get, but the percentage is revealed by scratching off that black stuff (what is that?) only after the purchase has been totaled at the cash register. The store is required to reveal(in
Spinner The plastic arrow on a spinner for a child’s game stops rotating to point at a color that will determine what happens next. Which of the following probability assignments are possible? Probabilities of... Red Yellow Green Blue a) 0.25 0.25 0.25 0.25 b) 0.10 0.20 0.30 0.40 c) 0.20 0.30
Jackpot On February 11, 2009, the AP news wire released the following story:(LAS VEGAS, Nev.)—A man in town to watch the NCAA basketball tournament hit a $38.7 million jackpot on Friday, the biggest slot machine payout ever. The 25-year-old software engineer from Los Angeles, whose name was not
Auto insurance Insurance companies collect annual payments from drivers in exchange for paying for the cost of accidents.a) Why should you be reluctant to accept a $1500 payment from your neighbor to cover his automobile accidents in the next year?b) Why can the insurance company make that offer?
Crash Commercial airplanes have an excellent safety record. Nevertheless, there are crashes occasionally, with the loss of many lives. In the weeks following a crash, airlines often report a drop in the number of passengers, probably because people are afraid to risk flying.a) A travel agent
Cold streak A basketball player missed 8 of 11 shots in the final portion of a game. When talking to reporters afterward, he says that he’s not worried about his next game because he’s due to make a lot of shots. Comment on his reasoning.
Snow After an unusually dry autumn, a radio announcer is heard to say, “Watch out! We’ll pay for these sunny days later on this winter.” Explain what he’s trying to say, and comment on the validity of his reasoning.
Winter Comment on the following quotation:“What I think is our best determination is it will be a colder than normal winter,” said Pamela Naber Knox, a Wisconsin state climatologist. “I’m basing that on a couple of different things. First, in looking at the past few winters, there has been
Rain The weather reporter on TV makes predictions such as a 25% chance of rain. What do you think is the meaning of such a phrase?
Roulette A casino claims that its roulette wheel is truly random. What should that claim mean?
Sample spaces For each of the following, list the sample space and tell whether you think the events are equally likely:a) Roll two dice; record the sum of the numbers.b) A family has 3 children; record each child’s sex in order of birth.c) Toss four coins; record the number of tails.d) Toss a
Sample spaces For each of the following, list the sample space and tell whether you think the events are equally likely:a) Toss 2 coins; record the order of heads and tails.b) A family has 3 children; record the number of boys.c) Flip a coin until you get a head or 3 consecutive tails;record each
Cell phones and surveys II The survey by the National Center for Health Statistics further found that 49% of adults ages 25–29 had only a cell phone and no landline.We randomly select four 25–29-year-olds:a) What is the probability that all of these adults have a only a cell phone and no

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