StatStudy Guide Exam 3
A probability experiment consists of rolling a fair 15-sided die. Find the probability of the event below. rolling a number divisible by 2
.467
The probability that an event will happen is Upper P left parenthesis Upper E right parenthesisequalsStartFraction 28 Over 31 EndFraction . Find the probability that the event will not happen.
3/31
When you calculate the number of combinations of r objects taken from a group of n objects what are you counting? Give an example.
You are counting the number of ways to select r of the n objects without regard to order. An example of a combination is the number of ways a group of teams can be selected for a tournament.
A basket contains 18 eggs, 7 of which are cracked. If we randomly select 8 of the eggs for hard boiling, what is the probability of the following events? a. All of the cracked eggs are selected. b. None of the cracked eggs are selected. c. Two of the cracked eggs are selected.
a. nCr=n!/(n-r)!r! P(A) = # ways can occure/#simple events) = s/n 18C8 = 43758 7c7= 1 11c1= 11 1x11=11 11/43758 = .0003 b. 7C0=1 11c8= 165 1x165= 165 165/43758 c. 7C2=21 11c6 = 462 21x462=9702 9702/43758 =.2217
A company is conducting a survey to determine how prepared people are for a long-term power outage, natural disaster, or terrorist attack. The frequency distribution on the right shows the results. Use the table to answer the following question. What is the probability that the next person surveyed is very prepared?
.115
The probability that an event will not happen is Upper P left parenthesis Upper E prime right parenthesisequals0.84. Find the probability that the event will happen.
.16
A probability experiment consists of rolling a fair 10-sided die. Find the probability of the event below. rolling a number greater than 8
.2
Use the pie chart at the right, which shows the number of tulips purchased from a nursery. Find the probability that a tulip bulb chosen at random is yellow.
.25
An individual stock is selected at random from the portfolio represented by the box-and-whisker plot shown to the right. Find the probability that the stock price is (a) less than $23, (b) between $23 and $57, and (c) $32 or more.
a.) .25 b.) .50 c.) .50
Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. If two events are independent, P(A|B)equalsP(B).
False; if events A and B are independent, then P(A and B)equalsP(A) times P(B).
A probability experiment consists of rolling a fair 10-sided die. Find the probability of the event below. rolling a 4
.1
Determine the number of outcomes in the event. Decide whether the event is a simple event or not. Upper A computer is used to select randomly a number between 1 and 9 comma inclusive. Event Upper C is selecting a number greater than 8.
1 yes exactly one
There are 56 runners in a race. How many ways can the runners finish first, second, and third?
56!/(56-3)!= 56x55x54=166320
Choose the three formulas that can be used to describe complementary events. Select the three formulas that can be used to describe complementary events.
P(E)+P(E')=1 P(E)=1-P(E') P(E')=1-P(E)
Sixteen of the 100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select a DVR that is not defective?
P(E)= #outcomes in event E/Total numer of outcomes in sample = .84
A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting a jack or four. (b) Compute the probability of randomly selecting a jack or four or five. (c) Compute the probability of randomly selecting a nine or diamond.
a. .154 b. .231 c. .308
Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation).
nCr= n!/(n-r)!r! = 43*42.../ (41*40...)2*1 = 43*42/2 =903
In order to conduct an experiment, 5 subjects are randomly selected from a group of 32 subjects. How many different groups of 5 subjects are possible?
nCr=N!/r!(n-r!) n=32 r= 5 = 32!/5!(32-5)! = 32x31x30x29x28/5! = 201376
Outside a home, there is an 8-key keypad with letters Upper A comma Upper B comma Upper C comma Upper D comma Upper E comma Upper F comma Upper G and Upper H that can be used to open the garage if the correct eight-letter code is entered. Each key may be used only once. How many codes are possible?
8x7x6x5x4x3x2x1= 40320
What does the notation P(B|A) mean?
The probability of event B occurring, given that event A has occurred
Use the bar graph below, which shows the highest level of education received by employees of a company, to find the probability that the highest level of education for an employee chosen at random is Upper E. The probability that the highest level of education for an employee chosen at random is Upper E is ________________
.061
How many different 10-letter words (real or imaginary) can be formed from the following letters? nbsp Upper T comma Upper N comma Upper A comma Upper A comma Upper D comma Upper E comma Upper N comma Upper D comma Upper T comma Upper N
10!/2!x3!x2!x2!x1!= 75600
Determine the number of outcomes in the event. Decide whether the event is a simple event or not. You randomly select one card from a standard deck of 52 playing cards. Event Upper B is selecting a red four. nothing nothing
2 outcomes no more than one
Determine which numbers could not be used to represent the probability of an event.
-1.5, because probability values cannot be less than 0. and 64/25, because probability values cannot be greater than 1.
Determine whether the statement is true or false. When an event is almost certain to happen, its complement will be an unusual event.
True, the complement would be an unusual event.
A coin is tossed and a six-sided die numbered 1 through 6 is rolled. Find the probability of tossing a head and then rolling a number greater than 5.
.083
A realtor uses a lock box to store the keys to a house that is for sale. The access code for the lock box consists of five digits. The first digit cannot be 3 and the last digit must be even. How many different codes are available? (Note that 0 is considered an even number.)
45000
The responses of 1405 voters to a survey about the way the media conducted themselves in a recent political campaign are shown in the accompanying Pareto chart. Find the probability of each event listed in parts (a) through (d) below.
Randomly selecting a person from the sample who did not give the media an A or a B: .759 Randomly selecting a person from the sample who gave the media a grade better than a D: .421 Randomly selecting a person from the sample who gave the media a D or an F: .579 Randomly selecting a person from the sample who gave the media a C or a D: .374
A study found that people who suffer from obstructive sleep apnea are at increased risk of having heart disease. Identify the two events described in the study. Do the results indicate that the events are independent or dependent?
Sleep apnea and heart disease dependent
Decide whether the events shown in the accompanying Venn diagram are mutually exclusive. Explain your reasoning.
The events are mutually exclusive, since there are no movies that are rated PG and are rated G.
The accompanying table shows the numbers of male and female students in a certain region who received bachelor's degrees in a certain field in a recent year. A student is selected at random. Find the probability of each event listed in parts (a) through (c) below.
The student is male or received a degree in the field: .519 REMEMBER TO SUBTRACT THE MALES IN FIELD The student is female or received a degree outside of the field: .904 The student is not female or received a degree outside of the field: .925
For the given pair of events, classify the two events as independent or dependent. Wearing no shoes or shirt Getting kicked out of a convenience store
The two events are dependent because the occurrence of one affects the probability of the occurrence of the other.
Of the cartons produced by a company, 6% have a puncture, 4% have a smashed corner, and 0.9% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner.
9.1%
Use the diagram to the right to answer the question. What is the probability that a registered voter did not vote in the election?
.536
Determine whether the statement is true or false. You toss a coin and roll a die. The event "tossing tails and rolling a 4 or 6" is a simple event.
False, the event is not simple because it consists of two possible outcomes.
When two pink flowers (RW) are crossed, there are four equally likely possible outcomes for the genetic makeup of the offspring: red (RR), pink(RW), pink(WR), and white (WW). If two pink snapdragons are crossed, what is the probability that the offspring will be (a) pink, (b) red, and (c) white?
If two pink snapdragons are crossed, the probability that the offspring will be pink is: .5 red: .25 white: .25
Use the frequency distribution to the right, which shows the number of voters (in millions) according to age, to find the probability that a voter chosen at random is in the given age range. not between 18 to 20 years old
.942
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Randomly choosing a multiple of 4 between 20 and 40 comma inclusive
20,24,28,32,36,40 there are 6 outcomes
A restaurant offers a $12 dinner special that has 6 choices for an appetizer, 12 choices for an entrée, and 4 choices for a dessert. How many different meals are available when you select an appetizer, an entrée, and a dessert?
288
Classify the following statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. An analyst feels that a certain stock's probability of increasing in price over the next month is 0.57.
subjective the stated probability is most likely based on intuition, an educated guess, or an estimate.
Determine whether the statement below is true or false. If it is false, rewrite it as a true statement. 7 Upper C 5 equals 7 Upper C 2
true
Determine whether the statement below is true or false. If it is false, rewrite it as a true statement. The number of different ordered arrangements of n distinct objects is n!.
true
A random number generator is used to select a number from 1 to 200 (inclusively). What is the probability of selecting the number 238?
0
Determine the number of outcomes in the event. Decide whether the event is a simple event or not. Upper A computer is used to select randomly a number between 1 and 9 comma inclusive. Event Upper A is selecting a number greater than 8.
1 outcome yes, because event a has exactly one outcome
A physics class has 40 students. Of these, 18 students are physics majors and 17 students are female. Of the physics majors, two are female. Find the probability that a randomly selected student is female or a physics major.
.825
(a) List an example of two events that are independent. (b) List an example of two events that are dependent.
a. Rolling a die twice b. Drawing one card from a standard deck, not replacing it, and then selecting another card
Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation). 59 Upper P 2 ! = product of whole numbers from 1 to n
(59!/57!) = not correct form but correct overall 3422 = 58*59; because those are the only factorials not included up to 57 nPr= n!/(n-r)!
Decide if the situation involves permutations, combinations, or neither. Explain your reasoning. The number of ways 12 people can line up in a row for concert tickets.
Permutations. The order of the 12 people in line matters.
A probability experiment consists of rolling a sixteen-sided die and spinning the spinner shown at the right. The spinner is equally likely to land on each color. Use a tree diagram to find the probability of the given event. Then tell whether the event can be considered unusual. Event: rolling a 9 and the spinner landing on green
.016 yes , because the probability is 0.05 or less.
A probability experiment consists of rolling a eight-sided die and spinning the spinner shown at the right. The spinner is equally likely to land on each color. Use a tree diagram to find the probability of the given event. Then tell whether the event can be considered unusual. Event: rolling a number less than 3 and the spinner landing on green
.063 D. No, because the probability is not close enough to 0.
Two cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a spade and then selecting a diamond.
.0637
A doctor gives a patient a 80% chance of surviving bypass surgery after a heart attack. If the patient survives the surgery, then the patient has a 55% chance that the heart damage will heal. Find the probability that the patient survives the surgery and the heart damage heals.
.44
What is the probability that a registered voter voted in the election?
.459
A physics class has 50 students. Of these, 17 students are physics majors and 18 students are female. Of the physics majors, seven are female. Find the probability that a randomly selected student is female or a physics major.
.560 you subtract the 7 female physics majors from the 17 (18/50)+(10/50)
Determine whether the following statement is true or false. If it is false, explain why. The probability that event A or event B will occur is Upper P left parenthesis Upper A or Upper B right parenthesis equals Upper P left parenthesis Upper A right parenthesis plus Upper P left parenthesis Upper B right parenthesis minus Upper P left parenthesis Upper A or Upper B right parenthesis.
False, the probability that A or B will occur is Upper P left parenthesis Upper A or Upper B right parenthesis equals Upper P left parenthesis Upper A right parenthesis plus Upper P left parenthesis Upper B right parenthesis minus Upper P left parenthesis Upper A and Upper B right parenthesis.
What is the difference between an outcome and an event?
An outcome is the result of a single probability experiment. An event is a set of one or more possible outcomes.
Classify the following statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. According to company records, the probability that a washing machine will need repairs during a nine-year period is 0.19.
Classical (or theoretical) probability is used when each outcome in a sample space is equally likely to occur. Empirical (or statistical) probability is based on observations obtained from probability experiments. Subjective probability results from intuition, educated guesses, and estimates. the stated probability is calculated based on observations from the company records.
The accompanying table shows the numbers of male and female students in a particular country who received bachelor's degrees in business in a recent year. Complete parts (a) and (b) below.
Find the probability that a randomly selected student is male, given that the student received a business degree: .515 business ans female: .159
The accompanying table shows the results of a survey in which 250 male and 250 female workers ages 25 to 64 were asked if they contribute to a retirement savings plan at work. Complete parts (a) and (b) below.
Find the probability that a randomly selected worker contributes to a retirement savings plan at work, given that the worker is male: .48 The probability that a randomly selected worker is female, given that the worker contributes to a retirement savings plan at work: .544
A stem-and-leaf plot for the number of touchdowns scored by all Division 1A football teams is shown below. Complete parts (a) through (c).
If a team is selected at random, find the probability the team scored at least 33 touchdowns: .619 If a team is selected at random, find the probability the team scored between 40 and 49 touchdowns inclusive: .254 If a team is selected at random, find the probability the team scored more than 79 touchdowns: Are any of these events unusual: Scoring more than 79 touchdowns is unusual.
A basket contains 15 eggs, 4 of which are cracked. If we randomly select 9 of the eggs for hard boiling, what is the probability of the following events? a. All of the cracked eggs are selected. b. None of the cracked eggs are selected. c. Two of the cracked eggs are selected.
NOT THE CORRECT WORK FOR THIS PROBLEM!! USE AS GUIDE a. nCr=n!/(n-r)!r! P(A) = # ways can occure/#simple events) = s/n 15C9 = 4c4= 1 9c5= 126 1x126=126 126/11440 = .0110 b. 7C0=1 11c8= 165 1x165= 165 165/43758 c. 7C2=21 11c6 = 462 21x462=9702 9702/43758 =.2217
The estimated percent distribution of a certain country's population for 2025 is shown in the accompanying pie chart. Find the probability of each event listed in parts (a) through (d) below. read the % on the chart
Randomly selecting someone who is under 5 years old: 4.3% Randomly selecting someone who is 45 years old or over: 44.4% Randomly selecting someone who is not 65 years old or over: 80.6 Randomly selecting someone who is between 20 and 34 years old: 19
Explain how the complement can be used to find the probability of getting at least one item of a particular type.
The complement of "at least one" is "none." So, the probability of getting at least one item is equal to 1minusP(none of the items).
Determine whether the events are independent or dependent. Explain your reasoning. Returning a rented movie after the due date and receiving a late fee
The events are dependent because the outcome of returning a rented movie after the due date affects the probability of the outcome of receiving a late fee.
Decide whether the events shown in the accompanying Venn diagram are mutually exclusive. Explain your reasoning. The events _______ mutually exclusive, since there _____________________ and _______________ presedential election
The events are not mutually exclusive, since there is at least 1 presidential candidate who lost the last pre dash election poll and lost the election
Determine whether the following problem involves a permutation or a combination and explain your answer. How many different 7-letter passwords can be formed from the letters Upper S, Upper T, Upper U, Upper W, Upper X, Upper Y, and Upper Z if no repetition of letters is allowed?
The problem involves a permutation because the order in which the letters are selected does matter.
Determine whether the statement below is true or false. If it is false, rewrite it as a true statement. A combination is an ordered arrangement of objects.
The statement is false. A true statement would be "A permutation is an ordered arrangement of objects."
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. You toss a fair coin nine times and it lands tails up each time. The probability it will land heads up on the tenth flip is greater than 0.5.
The statement is false. The correct statement is "You toss a fair coin nine times and it lands tails up each time. The probability it will land heads up on the tenth flip is exactly 0.5."
For the given pair of events, classify the two events as independent or dependent. Flipping a fair coin and getting tails Flipping the same coin again and getting heads
The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other.
Determine whether the following events are mutually exclusive. Explain your reasoning. Event A: Randomly select a voter who legally voted for the President in California. Event B: Randomly select a voter who legally voted for the President in Iowa.
These events are mutually exclusive, since it is not possible for a voter to both have legally voted for the President in California and have legally voted for the President in Iowa.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. If two events are mutually exclusive, they have no outcomes in common.
True
What is the difference between independent and dependent events?
Two events are independent when the occurrence of one event does not affect the probability of the occurrence of the other event. Two events are dependent when the occurrence of one event affects the probability of the occurrence of the other event.
A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting a heart or spade. (b) Compute the probability of randomly selecting a heart or spade or club. (c) Compute the probability of randomly selecting a ten or club.
a.) .5 = (13/52)+(13/52) b.) .75 c.) .308
Classify the following statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. The probability of choosing 6 numbers from 1 to 43 that match the 6 numbers drawn by a certain lottery is StartFraction 1 Over 6 comma 096 comma 454 EndFraction almost equals0.00000016.
classical every combination of 6 numbers has an equal chance of being drawn.
Classify the following statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. According to a survey, the probability that an adult chosen at random is in favor of police body cameras is about 0.43.
empirical the stated probability is calculated based on observations of adults' opinions.
You have 5 different video games. How many different ways can you arrange the games side by side on a shelf?
n!=n*(n-1)(n-2) 5*4*3*2*1 = 120 ways
At a blood drive, 4 donors with type Oplus blood, 3 donors with type Aplus blood, and 2 donors with type Bplus blood are in line. In how many distinguishable ways can the donors be in line?
n1= 4 n2= 3 n3=2 n!=nx(n-1)(n-2)(n-3)..... =9!/(4!x3!x2!) = 1260
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram. Determining an athlete's sport (baseball left parenthesis Upper B right parenthesis comma soccer left parenthesis Upper S right parenthesis comma football left parenthesis Upper F right parenthesis) and skill (low left parenthesis Upper L right parenthesis comma medium left parenthesis Upper M right parenthesis comma high left parenthesis Upper H right parenthesis)
{BL comma BM comma BH comma SL comma SM comma SH comma FL comma FM comma FH} 9 outcomes B s f lmh lmh lmh
At a blood drive, 5 donors with type Oplus blood, 4 donors with type Aplus blood, and 2 donors with type Bplus blood are in line. In how many distinguishable ways can the donors be in line?
n= 11 n1= 5 n2= 4 n3= 2 11!/5!x4!x2! = 6930
When you calculate the number of permutations of n distinct objects taken r at a time, what are you counting?
The number of ordered arrangements of n objects taken r at a time.
You roll a six-sided die. Find the probability of each of the following scenarios. (a) Rolling a 6 or a number greater than 3 (b) Rolling a number less than 5 or an even number (c) Rolling a 6 or an odd number
a. .5 ((1/6)+(3/6))-(1/6) b. .833 (5/6) c. .667 (4/6)
A physics class has 40 students. Of these, 16 students are physics majors and 17 students are female. Of the physics majors, seven are female. Find the probability that a randomly selected student is female or a physics major.
.650
Use the pie chart at the right, which shows the number of workers (in thousands) by industry for a certain country. Find the probability that a worker chosen at random was not employed in the manufacturing industry.
.891
An archaeology club has 29 members. How many different ways can the club select a president, vice president, treasurer, and secretary?
29!/(29-4)! = 29x28x27x26= 570024
Of the cartons produced by a company, 3% have a puncture, 4% have a smashed corner, and 0.5% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner.
6.5% ((3/100)+(4/100))-(.5/100)=.065=6.5%
The table below shows the results of a survey that asked 1052 adults from a certain country if they favored or opposed a tax to fund education. A person is selected at random. Complete parts (a) through (c).
Find the probability that the person opposed the tax or is female: .826 REMEMBER TO SUBTRACT THE FEMALES WHO OPOSED THE BILL Find the probability that the person supports the tax or is male: .692 Find the probability that the person is not unsure or is female: .986
If two events are mutually exclusive, why is Upper P left parenthesis Upper A and Upper B right parenthesis equals 0?
P(A and B)=0 because A and B cannot occur at the same time.
The access code for a gym locker consists of three digits. Each digit can be any number from 0 through 7, and each digit can be repeated. Complete parts (a) through (c). (a) Find the number of possible access codes. (b) What is the probability of randomly selecting the correct access code on the first try? (c) What is the probability of not selecting the correct access code on the first try?
The number of different codes available is: 512 The probability of randomly selecting the correct access code is: .002 not selecting: .998
In a recent year, about 37% of all infants born in a country were conceived through in-vitro fertilization (IVF). Of the IVF deliveries, about twenty-six percent resulted in multiple births. (a) Find the probability that a randomly selected infant was conceived through IVF and was part of a multiple birth. (b) Find the probability that a randomly selected infant conceived through IVF was not part of a multiple birth. (c) Would it be unusual for a randomly selected infant to have been conceived through IVF and to have been part of a multiple birth? Explain.
The probability that a randomly selected infant was conceived through IVF and was part of a multiple birth is: .096 The probability that a randomly selected infant conceived through IVF was not part of a multiple birth is: .74 No, this is not unusual because the probability is not less than or equal to 0.05.
The probability that a person in the United States has type B+ blood is 7%. Four unrelated people in the United States are selected at random. Complete parts (a) through (d).
The probability that all four have type B+ blood is: .000024 Find the probability that none of the four have type B+ blood.:.748 Find the probability that at least one of the four has type B+ blood: .252 The event in part left parenthesis a right parenthesis is unusual because its probability is less than or equal to 0.05.
In a sample of 1200 U.S. adults, 208 think that most celebrities are good role models. Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S. adults, complete parts (a) through (c).
The probability that both adults think most celebrities are good role models is: .030 The probability that neither adult thinks most celebrities are good role models is: .683 The probability that at least one of the two adults thinks most celebrities are good role models is: 1-.683= .317
In order to conduct an experiment, 4 subjects are randomly selected from a group of 51 subjects. How many different groups of 4 subjects are possible?
n=51 51x50x49x48/4x3x2x1 = 249900