STATISTICS CHAP 4, 5 ,6, 7
How many three-digit odd numbers can be formed from the digits 2, 3, 5, 8, 9 if repetition of digits is not allowed?
CHAPTER 4 36
In how many ways can 6 teachers be assigned to 4 different classes?
CHAPTER 4 360
Allan, Berna, Chad, Denise, Echo, Farida and Gerald are to be seated in a row of 7 chairs. In how many ways can we arrange them such that Denise and Gerald are not seated next to each other?
CHAPTER 4 3600
In how many ways can we select 5 cards from a standard deck such that it consists of a three of a kind and a two of a kind?
CHAPTER 4 3744
There are 4 families, each consisting of a mother, a father and an only child. In how many ways can we arrange them in a row of seats such that members of the same family are seated together with the only child seated in the middle of the parents?
CHAPTER 4 384
In how many ways can a student answer 5 multiple choice questions, with four choices each with only one correct answer, such that the student gets exactly 2 questions correctly?
CHAPTER 4 270
In how many ways can we arrange the letters of the word "PAPAS"?
CHAPTER 4 30
One thousand students from the COS, CCS and were asked about their preferred sizes of shirt. The following contingency table gives the result. COS CCS COE Small 89 110 92 Medium 102 78 123 Large 113 128 165 If a student is selected at random, what is the probability the the student is from CCS?
316/1000
How many ways can a basketball team end an elimination round of 14 games with 6 wins and 8 losses?
CHAPTER 4 3003
In how many ways can 8 runners win the top three medals (Gold, Silver, Bronze) in a race, assuming that each race time is different?
CHAPTER 4 336
A college freshman must take a science course, a humanities course and a mathematics course. If she may select any of 6 science courses, any of 4 humanities courses and any 4 of mathematics courses, how many possible programs can she make?
CHAPTER 4
A soccer team plays eight games during a league. Each game will result to a win, loss or draw. A. In how many ways can the soccer team end the season with five wins and three draws? B. In how many ways can the soccer team end with four wins, two draws and two losses? C. In how many ways can the soccer team end with no loss?
CHAPTER 4
A teacher constructed a test in which the first part is composed of five true-or-false questions and the second part is composed of five multiple-choice questions, each of which has five options. In how many ways can a student answer this test?
CHAPTER 4
A witness to a hit-and-run accident told the investigator that the plate number of the suspect's car contained the letters ZE followed by another letter, and then followed by three digits which are distinct, what is the maximum number of automobile registrations that the police may have to check?
CHAPTER 4
An experiment consists of throwing a die and then selecting a letter from the English alphabet. How many elements are there in the sample space S of this experiment?
CHAPTER 4
Angie has to answer any six problems on a test consisting of ten problems. A. In how many different ways can she select at least six problems? B. In how many different ways can she select at most six problems?
CHAPTER 4
Consider the digits 2, 3, 5, 6 and 8. A. How many three-digit numbers can be formed if repetition of digits is allowed? B. How many three-digit numbers can be formed if repetition of digits is not allowed? C. How many three-digit numbers that is greater than 300 if repetition of digits is allowed?
CHAPTER 4
Consider the word "probsta". In how many ways can we arrange the letters of the given word such that A. The permutation begins with a consonant. B. The permutation ends with a vowel. C. The second and fourth letters must be a consonant.
CHAPTER 4
Find the number of ways in which 6 programmers can be assigned to 4 projects if no programmer is assigned to more than one project?
CHAPTER 4
From a group of 4 men and 5 women, how many committees of size 3 are possible A. with no restrictions? B. with 1 man and 2 women? C. with at least 2 women?
CHAPTER 4
How many permutations can we obtain from the letters of the following words? A. Sample B. Mississippi
CHAPTER 4
How many ways are there to select 3 candidates from 8 equally qualified recent graduates for openings in an IT firm
CHAPTER 4
In a certain university, students are classified according to their year level (F, So, Jr, Sr) and to the college that they belong in (COS, CCS, COE, CLA, COB, CED). How many types of students are there in the university?
CHAPTER 4
In a party, ten chairs are positioned around a circular table. A. In how many ways can ten people be seated around the table? B. In how many ways can ten people be seated around the table if three insist on seating next to each other? C. In how many ways can ten people be seated around the table if three of them refuse to be seated next to one another?
CHAPTER 4
In a standard deck of 52 playing cards, 5 cards are selected. How many possible selections will contain A. A full house consisting of Two aces and three kings B. Exactly 2 face cards C. At least 3 queen cards D. At most three non-face cards
CHAPTER 4
In how many different ways can a true or false exam consisting of 9 questions be answered without leaving any item unanswered?
CHAPTER 4
In how many ways can 5 people be seated together in a row such that two people, Paolo and Mae, do not want to be seated next to each other?
CHAPTER 4
In how many ways can a test consisting of 12 multiple choice questions (each with four choices and only one correct answer) be answered such that A. all the questions are answered incorrectly. B. the items numbered 1, 5, 7 and 11 are answered correctly and the other numbers incorrectly. C. exactly 4 questions are answered correctly.
CHAPTER 4
In how many ways can four boys and five girls sit in a row if boys and girls must alternate?
CHAPTER 4
In how many ways can three men and five women be seated in a circular manner if A. The men and women are together B. One of the women and one of the men refuse to sit together
CHAPTER 4
To play a certain raffle, you select six numbers from 1 to 42. You win the grand prize if your six numbers match the six winning numbers drawn. A. How many possible combinations are there? B. In how many ways can you select the six winning numbers and win the jackpot prize? C. You still win a consolation prize if you select five winning numbers and four winning numbers. In how many ways can you win a consolation prize
CHAPTER 4
Twelve officers of an organization are to be divided into committees. A. In how many ways can the officers be divided into three committees composed of four members each? B. In how many ways can the officers be divided into three committees composed of six, four, and two members, respectively?
CHAPTER 4
Allan, Berna, Chad, Denise, Echo, Farida and Gerald are to be seated around a circular table. In how many ways can we arrange them such that Denise, Gerald and Allan are seated next to each other?
CHAPTER 4 144
An experiment consists of selecting three cards, one at a time, from a standard deck without replacement. In how many ways can we select the three cards such that it consists of a card from 2 to 8 and two face cards?
CHAPTER 4 1848
Alyana has 6 spaces for her toys and Robert has 4. In how many ways can 9 toys be distributed to them?
CHAPTER 4 210
In how may ways can 5 students be selected from 10 students to form a committee?
CHAPTER 4 252
There are 4 white pillows, 3 blue pillows and 3 red pillows in a store. If these pillows are to be arranged in a row, how many different arrangements are possible if pillows of the same color are indistinguishable from each other?
CHAPTER 4 4200
An experiment consists of selecting three cards, one at a time, from a standard deck with replacement. In how many ways can we select the three cards such that it consists of 2 face cards and an ace.
CHAPTER 4 576
Sab is creating a birthday party menu consisting of 4 appetizers, 5 main dishes and 3 desserts. How many different menus are possible?
CHAPTER 4 60
A box has 10 fuses and 3 of them are defective. In how many ways can we select 4 fuses such that at least two of them are defective?
CHAPTER 4 70
How many different permutations of the word "POLAND" are possible?
CHAPTER 4 720
An experiment consists of tossing a coin: If a head occurs, the same coin is tossed once. If a tail occurs, the same coin is tossed twice. Which of the following is NOT an element of the sample space?
CHAPTER 4 HTT
An experiment consists of tossing a coin, rolling a pair of dice and selecting a card from a standard deck of playing cards. How many possible outcomes are there?
CHAPTER 4 3744
A box contains 20 computer chips, 4 of which are defective. If 3 are selected at random, what is the probability that A. All are defective? B. At most one is defective?
CHAPTER 5
A box contains 4 black balls and 3 white balls, and another box contains 7 white balls and 3 black balls. If one ball is drawn from each box, what is the probability that the two balls are of different colors?
CHAPTER 5
A committee of 5 members will be chosen from a group of 10 teachers and 5 students. What is the probability that the committee will have A. All teachers? B. 3 teachers and 2 students? C. 3 or 4 teachers? D. From 1 to 3 students?1
CHAPTER 5
A jar contains 6 red balls, 3 green balls, 5 white balls and 7 yellow balls. Two balls are chosen from the jar, with replacement. What is the probability that both balls chosen are green?
CHAPTER 5
A sample of 500 respondents was selected in a large city to determine information about consumer behavior. One of the questions asked was "Do you enjoy shopping for clothing?" Enjoys Shopping Male Female YES 136 224 NO 104 36
CHAPTER 5
Consider the word "problem". What is the probability that a permutation of the word "problem" A. begins with a vowel? B. ends with a consonant?
CHAPTER 5
Four friends, Mark, Paolo, Kiko and JV decided to meet at Starbucks in Makati. Assuming that there are only four Starbucks outlets in the said city, what is the probability that A. all of them will meet in the same Starbucks outlet? B. three of the four will meet in the same Starbucks outlet and Mark is in another Starbucks outlet.
CHAPTER 5
If 6 balls are drawn without replacement from a bag that contains 7 black and 5 white balls, what is the probability that A. four will be black and 2 will be white? B. less than two white balls will be selected? C. There is at least one green black ball
CHAPTER 5
If an individual is chosen randomly from this group, find the probability that the person is A. a male and does not enjoy shopping B. a female or enjoys shopping C. does not enjoy shopping D. does not enjoy shopping given the consumer is a female
CHAPTER 5
In New York State, 48% of all teenagers own a skateboard and 39% of all teenagers own a skateboard and roller blades. What is the probability that a teenager owns roller blades given that the teenager owns a skateboard?
CHAPTER 5
In a 12-item multiple choice examination (each with four choices of which only one is correct), what is the probability of getting only 4 mistakes assuming that no question is left unanswered?
CHAPTER 5
In a class of 30 students, there are 17 girls and 13 boys. Five are A students, and three of these students are girls. If a student is chosen at random, what is the probability of choosing a girl or an A student?
CHAPTER 5
In a standard deck of 52 playing cards, 5 cards are to be selected. What is the probability that the cards selected contains A. two kings and three jacks? B. three heart cards? C. at least three queens?
CHAPTER 5
In a standard deck of 52 playing cards, a card is to be selected. What is the probability that the card selected is a spade given that the card is a king, queen or jack?
CHAPTER 5
In a university, 30% of the students major in Business Management, 25% major in Mathematics, and 10% major in both Business Management and Mathematics. A student from this university is selected at random. A. What is the probability that the student majors in Business Management or Mathematics? B. What is the probability that the student majors in neither of these two courses? C. If the student majors in Business Management, what is the probability that he/she also majors in Mathematics?
CHAPTER 5
In selecting a card from a standard deck of 52 playing cards, what is the probability of getting a heart card and at the same time a face card?
CHAPTER 5
In the United States, 43% of people wear a seat belt while driving. If two people are chosen at random, what is the probability that both of them wearing a seat belt?
CHAPTER 5
In tossing three coins, what is the probability of getting A. exactly two heads? B. at least two heads
CHAPTER 5
One bag contains 11 yellow balls and 7 blue balls and a second bag contains 8 yellow balls and 9 blue balls. One ball is drawn from the first bag and placed unseen in the second bag. What is the probability that a ball now drawn from the second bag is blue?
CHAPTER 5
Spin a spinner numbered 1 to 7, and toss a coin. What is the probability of getting an odd number on the spinner and a tail on the coin?
CHAPTER 5
Suppose that a bread manufacturing industry has three inspectors to stamp the expiration date on each package of bread. Ken, who stamps 20% of the packages, fails to stamp the expiration date once every 100 packages. Jen, who stamps 60% of the packages, fails to stamp once in every 200 packages. Kat, who stamps 20% of the packages, fails to stamp once in every 150 packages. A. What is the probability of getting a package with no expiration date? B. If a package has no expiration date, what is the probability that it was inspected by Jen? C. If a package has no expiration date, what is the probability that it was inspected by Ken or Kat?
CHAPTER 5
Suppose that a company classifies 80% of its employees with good attendance and the rest with bad attendance. An employee is classified with good attendance if he/she is present and punctual 98% of the time. An employee is said to be with bad attendance if he/she is absent and late 30% of the time. What percentage of the total absences hold by employees classified as with bad attendance?
CHAPTER 5
Suppose that in a certain town with a population of 5000 households, 3000 of the households have cell phone, 2000 have computers at home, and 1500 have both cell phones and computers. A household in the town is selected at random. A. What is the probability that the selected household owns a cell phone or a computer? B. What is the probability that the household does not own a cell phone or a computer? C. If the household owns a cell phone, what is the probability that it also owns a computer? D. If the household owns a cell phone, what is the probability that it does not own a computer? E. Is owning a cell phone independent of having a computer at home? Why?
CHAPTER 5
The probability that a man will live until 70 years is ¾ and the probability that his wife will live until 70 years is 4/5. What is the probability that A. Both will live until 70 years B. At least one will live until 70 years C. None will live until 70 years
CHAPTER 5
A basketball player free throw shooting percentage is 65%. This player is about to shoot two free throws. What is the probability that the player makes both free throws, assuming that each attempt is independent from each other?
CHAPTER 5 0.4225
One thousand students from the COS, CCS and were asked about their preferred sizes of shirt. The following contingency table gives the result. COS CCS COE Small 89 110 92 Medium 102 78 123 Large 113 128 165 If a student is selected at random, what is the probability the the student prefers Small size of shirt given that he/she is from CCS?
CHAPTER 5 110/316
In the Philippine 6/45 lotto system, what is the probability that a player's bet would get exactly 4 of the winning numbers?
CHAPTER 5 11115/8145060
One thousand students from the COS, CCS and were asked about their preferred sizes of shirt. The following contingency table gives the result. COS CCS COE Small 89 110 92 Medium 102 78 123 Large 113 128 165 If a student is selected at random, what is the probability the the student is from COS and prefers Large size of shirt?
CHAPTER 5 113/1000
One thousand students from the COS, CCS and were asked about their preferred sizes of shirt. The following contingency table gives the result. COS CCS COE Small 89 110 92 Medium 102 78 123 Large 113 128 165 If a student is selected at random, what is the probability the student is from COE given that he/she prefers Medium size of shirt?
CHAPTER 5 123/303
In a room, there are 13 men and 7 women. If a person is randomly selected, what is the probability of selecting a man?
CHAPTER 5 13/20
Suppose that two balls are selected with replacement from a bag that contains 10 white and 5 black balls. What is the probability that both balls are black?
CHAPTER 5 25/225
What is the probability that a four-digit number formed from the digits 3, 5, 6, 7, 8 is even if repetition of digits is allowed? Type answer in fraction form:
CHAPTER 5 250/625
What is the probability that a permutation of the word "PORTUGAL" begins with a consonant?
CHAPTER 5 25200/40320
Four couples are about to watch a movie together. What is the probability that, on 8 available row seats, each couple are seated together?
CHAPTER 5 384/40320
What is the probability that a four-digit number formed from the digits 3, 5, 6, 7, 8 is even if repetition of digits is NOT allowed?
CHAPTER 5 48/120
What is the probability of selecting 5 balls from a bag containing 4 red and 9 blue balls such that the selection has exactly 3 blue balls?
CHAPTER 5 504/1287
A shipment of 7 television sets contains 2 defectives. A hotel makes a random purchase of 3 of these sets. If X is the random variable representing the number of defective sets purchased by the hotel, A. Construct the probability mass function of the random variable X. B. Find the mean, variance and standard deviation of X. C. What is the probability that at least two defective television sets are selected?
CHAPTER 6
By investing in a particular stock, a person can make a profit in 1 year of $4000 with probability 0.4 or take a loss of $1000 with probability 0.6. What is this person's expected profit?
CHAPTER 6
In a game of selecting a card from a standard deck of 52 playing cards, a player wins $50 if a heart card is selected. Otherwise, a player loses. In order to play the game, a player should pay $10. What is the expected net gain of the player? Is this game fair? Why or why not?
CHAPTER 6
Let X be a random variable with the following probability mass function. Find the mean of the random variable X. 𝑿 0 1 2 3 𝒑(𝒙) 𝟖 /𝟐𝟕 ? 𝟐 /𝟗 𝟏 /𝟐𝟕 A. Find the probability 𝑷(𝑿 = 𝟏). B. Find the mean, variance and standard deviation of X.
CHAPTER 6
The probability distribution of the discrete random variable X is given by the formula 𝒑(𝒙) = (𝟑 𝒙 )( 𝟏 𝟒 ) 𝒙 ( 𝟑 𝟒 ) 𝟑−𝒙 ,𝒙 = 𝟎,𝟏,𝟐,𝟑 A. Construct the probability mass function of the random variable X. B. Find the mean, variance and standard deviation of X. C. Determine 𝑷(𝟏 ≤ 𝑿 ≤ 𝟐).
CHAPTER 6
Using the company records for the past 500 working days, the manager of Konig Motors, a suburban automobile dealership, has summarized the number of cars sold per day into the following table: Number of Card Sold Per Day 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 Frequency 40, 100, 142, 66, 36, 30, 26, 20, 16, 14, 8, 2 A. Form the probability mass function for the random variable X that represents the number of cars sold per day. B. Compute the mean, variance and standard deviation of the random variable X. C. What is the probability that on any given day, fewer than four cars will be sold? D. What is the probability that on any given day, at most four cars will be sold? E. What is the probability that on any given day, at least four cars will be sold? F. What is the probability that on any given day, exactly four cars will be sold? G. What is the probability that on any given day, more than four cars will be sold?
CHAPTER 6
A baseball player's batting chance is 0.25. What is the probability that he gets A. Exactly one hit in his next 5 times at bat? B. At most 2 hits in his next 5 times at bat? C. Find the mean and standard deviation of the random variable X.
CHAPTER 7
A restaurant prepares a tossed salad containing on the average 5 vegetables. Find the probability that the salad contains more than 5 vegetables A. on a given day. B. on 3 of the next 4 days
CHAPTER 7
A secretary makes two errors per page on the average. A. What is the probability that on the next page, she makes four or more errors? B. What is the probability that in the next two pages, she makes no errors?
CHAPTER 7
According to the United National Environmental Program and World Health Organization, in Mumbai, India, air pollution standards for particulate matter are exceeded an average of 5.6 days in every three-week period. Assume that the distribution of number of days exceeding the standards per three-week period is Poisson distributed. A. What is the probability that the standards are not exceeded on any day during a three-week period? B. What is the probability that the standards are exceeded exactly six days of a one-week period? C. What is the probability that the standards are exceeded 10 or more days during a two-week period?
CHAPTER 7
Five percent of the laptops manufactured by ABC Technologies have some defects. A. What is the probability that exactly three in a sample of ten laptops manufactured by ABC technologies have some defects? B. What is the probability that the tenth laptop to be inspected is the third one that has some defects? C. What is the probability that the tenth laptop to be inspected is the first one that has some defects?
CHAPTER 7
From a lot of 12 missiles, 5 are selected at random and fired. If the lot contains 3 defective missiles that will not fire, what is the probability that A. all 5 will fire? B. at most 2 will not fire? C. Find the mean and variance of the random variable X that represents the number of missiles that will fire from the 5 missiles selected.
CHAPTER 7
Rechel, a bank teller, knows from experience that 40% of customers entering the bank will make a cash withdrawal. What is the probability that on any given banking day, the tenth customer to enter the bank will be A. the third customer to make a cash withdrawal? Determine the mean and variance. B. the first customer to make a cash withdrawal? Determine the mean and variance.
CHAPTER 7
The Wall Street Journal reported some interesting statistics on the job market. One statistic is that 40% of all workers say they would change jobs for "slightly higher pay". In addition, 88% of companies say that there is a shortage of qualified job candidates. Suppose 16 workers are randomly selected and asked if they would change jobs for "slightly higher pay." A. What is the probability that nine or more say yes? B. What is the probability that 3, 4, 5, or 6 say yes? C. If 13 companies are contacted, what is the probability that exactly 10 say there is a shortage of qualified job candidates?
CHAPTER 7
The probability that a patient recovers from a delicate heart operation is 0.9. What is the probability that exactly 5 of the next 7 patients having this operation survive? Find the mean and variance of the random variable X.
CHAPTER 7
What is the probability that a waitress will refuse to serve alcoholic beverages to 2 minors if she randomly checks the ID's of 6 students from among 9 students of which 4 are not of legal age? Find the mean and standard deviation of the random variable X.
CHAPTER 7
