Deck 4: Probability: the Study of Randomness

Question 1

Football is a very popular sport in the United States.The National Football League (NFL)is composed of 32 teams.Every year there is a football draft where players are selected for each of the teams.Football players in the United States can make millions of dollars and must be very good at the sport to make a team.Would being selected for an NFL team be considered a random phenomenon?

A)Yes,everyone is probably very good at football and would qualify for a team.
B)Yes,there are a large number of teams,which makes this a random phenomenon.
C)No,there are probably certain skill sets necessary for football that owners of teams are looking for in players.
D)No,if you really want to play football,you can probably join an NFL team.

Answer 1

No,there are probably certain skill sets necessary for football that owners of teams are looking for in players.

Question 2

Which of the following is/are appropriate statements about randomness and/or probability?

A)A phenomenon is called random if individual outcomes are uncertain,but in a large number of repetitions,there is a regular distribution of outcomes.
B)The word random in statistics is a description of a kind of order that emerges in the long run.
C)Probability describes only what happens in the long run.
D)In a small or moderate number of repetitions,the observed proportion of an outcome can be far from the probability of the outcome.
E)All of the above are appropriate statements.

Answer 2

All of the above are appropriate statements.

Question 3

The probability of an event is defined as the proportion of times an event occurs occasionally.

Answer 3

False

Question 4

In a certain game you have to guess the number that your opponent writes down on a sheet of paper.You get five guesses.After each guess,your opponent has to tell you if your number is too high or too low.Each guess is considered ________ the last guess.

A)independent of
B)dependent on

Question 5

There is a popular pizza restaurant on campus that many students frequent.One evening,your college sorority goes to the restaurant to celebrate the end of the semester.At the end of the evening,you are not feeling well and several of your sorority sisters do not feel well either.You suspect food poisoning from the restaurant is the culprit.Suppose your roommate is also sick and ate at the same restaurant on the same day as you.Would your roommate being sick be an example of a random phenomenon?

A)Yes,because more than one person is sick it must be a random phenomenon.
B)Yes,because you went to a random restaurant on campus.
C)No,since your roommate ate at the same restaurant,it is probably not a random phenomenon that she is sick.
D)No,everyone at the restaurant would have to be sick for it to be a random phenomenon.

Question 6

You decide you want to start a garden and grow tomatoes and cucumbers.After a month the yield of the tomatoes and cucumbers is quite low.You dig up the plants and start again in the same plot.However,the next month the yield of the tomatoes and cucumbers is still quite low.The yield of the tomatoes and cucumbers from month 1 to month 2 is considered __________.

A)independent
B)dependent

Question 7

The statistics of a particular basketball player state that he makes 4 out of 5 free-throw attempts.During a season,the basketball player makes an average of about 200 free-throw attempts.On how many of these throws would you estimate he will actually score a point?

A)80
B)100
C)120
D)160

Question 8

Checkers is a board game played between two players,who alternate moves.The board is square,with sixty-four smaller squares,arranged in an eight-by-eight grid.The smaller squares are alternately light and dark colored,in the famous "checker-board" pattern.Each player starts with 12 pieces.You win by capturing all your opponent's pieces.This is accomplished by jumping over a piece,diagonally,to the adjacent vacant square beyond the piece.If each player's goal is to win the game,then each move is considered _________.

A)independent
B)dependent

Question 9

A phenomenon is observed many,many times under identical conditions.The proportion of times a particular event A occurs is recorded.What does this proportion represent?

A)The probability of the event A
B)The distribution of the event A
C)The correlation of the event A
D)The variance of the event A

Question 10

For an event to be random (e.g. ,flipping a coin five times),a cluster of the same observations (e.g. ,all heads)would not be possible.

Question 11

If you have a fair die,what is the expected proportion of rolls that result in a number greater than 4?

A)1/6
B)1/3
C)2/3
D)1/2

Question 12

In a certain game you have to guess the number that your opponent writes down on a sheet of paper.You get five guesses and no additional information is given after each guess unless it is the correct number.Each guess is considered _______ the last guess.

A)independent of
B)dependent on

Question 13

The game of craps starts with a "come-out" roll,in which the shooter rolls a pair of dice.If the total of the "spots" on the up-faces is 2,3,or 12,the shooter loses immediately.What is the proportion of come-out rolls that ends up in an immediate loss for the shooter?

A)1/9
B)¹/₄
C)8/9
D)1/12

Question 14

The statistics of a particular basketball player state that he makes 4 out of 5 free-throw attempts.The basketball player is just about to attempt a free throw.What do you estimate the probability that the player makes this next free throw to be?

A)0.16
B)50-50-either he makes it or he doesn't.
C)0.80
D)1.2

Question 15

A penny is tossed.We observe whether it lands heads up or tails up.Suppose the penny is a fair coin;that is,the probability of heads is one-half and the probability of tails is one-half.What does this mean?

A)Every occurrence of a head must be balanced by a tail in one of the next two or three tosses.
B)If the coin is tossed many,many times,the proportion of tosses that land heads will be approximately one-half,and this proportion will tend to get closer and closer to one-half as the number of tosses increases.
C)Regardless of the number of flips,one-half will be heads and one-half tails.
D)All of the above

Question 16

Which of the following best describes what is meant by the probability of the outcome of a random phenomenon?

A)The count of the short-term occurrences of the outcomes
B)The count of the outcomes of the phenomenon that occur in a haphazard manner
C)The proportion of outcomes that can be expected to be observed during a short experiment
D)The proportion of times the outcome would occur in a very long series of repetitions
E)The proportion of repetitions that result in the outcome when an experiment is conducted about the random phenomenon

Question 17

There are five upper-level mathematics courses that are required for math majors at a certain university.You can only pass the last course after you have passed all of the other four.Passing the last course is considered a(n)________ event.

A)independent
B)dependent

Question 18

You are taking a basic statistics class.On the first exam you score poorly and receive only 10 out of 100 points.You decide to get a tutor for the next exam and study quite a bit more.You end up scoring much better and receive 80 out of 100 points.The scores on your first and second exam are considered _________.

A)independent
B)dependent

Question 19

To win the Maryland Powerball^® Lottery,you must select your own six numbers to play.Most people use numbers that are special to them,like anniversary dates or their children's birth dates.On the day of the lottery,the lottery officials randomly select five white balls,each with a number somewhere between 1 and 59,and one red Powerball^® with a number somewhere between 1 and 35.You win a prize by matching some or all of the numbers drawn.Would winning the lottery be an example of a random phenomenon?

A)Yes,because the numbers drawn are random
B)Yes,because you are selecting your own six numbers to play
C)No,because the numbers you select to play are not random if you choose your anniversary date or your children's birth dates
D)No,because the numbers drawn are random

Question 20

Which of the following are independent trials?

A)The results of a coin flip after rolling two dice
B)The first character of a license plate and the color of the car
C)The total of two dice after recording the value of the first die rolled
D)A and B
E)All of the above

Question 21

The United States has 10 federal holidays.Each holiday and the date of the holiday in 2016 are listed in the table below. Suppose you employer allows you to take up to three of the federal holidays off from work.What is the sample space for the number of federal holidays you take off?

A)S = {0,1,2,3}
B)S = {3}
C)S = {Veterans,Thanksgiving,Christmas,New Year's,Martin Luther King,Washington,Memorial,Independence,Labor,Columbus}
D)None of the above

Question 22

Suppose you have a perfectly fair 10-sided die,with sample space S = {1,2,3,4,5,6,7,8,9,10}.What are the probabilities of each possible outcome?

A)All probabilities are equal to ¹/₂.
B)P(1)= P(2)= P(3)= P(4)= P(5)= P(6)= P(6)= P(7)= P(8)= P(9)= P(10)= 1/10
C)P(1)= P(2)= P(3)= P(4)= P(5)= P(6)= P(6)= P(7)= P(8)= P(9)= P(10)= 1/6
D)None of the above

Question 23

The United States has 10 federal holidays.Each holiday and the date of the holiday in 2016 are listed in the table below. Suppose your employer only allows you take three of the federal holidays off from work.What is the sample space for the federal holidays you take off?

A)S = {0,1,2,3}
B)S = {3}
C)S = {Veterans,Thanksgiving,Christmas,New Year's,Martin Luther King,Washington,Memorial,Independence,Labor,Columbus}
D)None of the above

Question 24

Suppose Team A has a 0.75 probability to win their next game and Team B has a 0.85 probability to win their next game.Assume these events are independent.What is the probability that Team A wins exactly two of their next three games?

A)0.18750
B)0.140625
C)0.421875
D)1.5

Question 25

The United States has 10 federal holidays.Each holiday and the date of the holiday in 2016 are listed in the table below. You work in Washington,DC,and you are looking forward to enjoying the day off on the federal holidays.There are high chances of snow in Washington,DC,from November to March.What is the sample space for the federal holidays that could occur during a winter snow storm in Washington,DC?

A)S = {Jan,Feb,Mar,Apr,May,Jun,Jul,Aug,Oct,Nov,Dec}
B)S = {Nov,Dec,Jan,Feb}
C)S = {Veterans,Thanksgiving,Christmas,New Year's,Martin Luther King,Washington}
D)S = {Veterans,Thanksgiving,Christmas,New Year's,Martin Luther King,Washington,Memorial,Independence,Labor,Columbus}

Question 26

Suppose Team A has a 0.75 probability to win their next game and Team B has a 0.85 probability to win their next game.Assume these events are independent.What is the probability that both Team A and Team B win?

A)1.60
B)0.6375
C)0.85
D)0.75

Question 27

A standard deck of cards has 52 cards.The cards have one of two colors: 26 cards in the deck are red and 26 are black.The cards have one of four denominations: 13 cards are hearts (red),13 cards are diamonds (red),13 cards are clubs (black),and 13 cards are spades (black).One card is selected at random and the denomination is recorded.Which of the following is the correct sample space S for the set of possible outcomes?

A)S = {red,black}
B)S = {red,red,black,black}
C)S = {hearts,diamonds,clubs,spades}
D)S = {red,black,hearts,diamonds,clubs,spades}

Question 28

Which of the following define a complete and valid probability model?

A)S = {A,B,C};P(A)= 1/3,P(B)= 2/3,P(C)= 1
B)S = {H,T};P(H)= 1/4,P(T)= ³/₄
C)S = {W,X,Y,Z};P(W)= ¹/₄,P(X)= 1/4,P(Z)= ¹/₄
D)P(RED)= 1/2,P(BLUE)= ¹/₂

Question 29

A standard deck of cards has 52 cards.The cards have one of two colors: 26 cards in the deck are red and 26 are black.The cards have one of four denominations: 13 cards are hearts (red),13 cards are diamonds (red),13 cards are clubs (black),and 13 cards are spades (black).Two cards are selected at random and the denomination is recorded.The event H is defined as the event that the first card is hearts.Which of the following correctly defines event H?

A)H = {diamonds,clubs,spades}
B)H = {hearts,diamonds,clubs,spades}
C)H = {(hearts,diamonds), (hearts,clubs), (hearts,spades)}
D)H = {(hearts,diamonds), (hearts,clubs), (hearts,spades), (hearts,hearts)}

Question 30

A standard deck of cards has 52 cards.The cards have one of two colors: 26 cards in the deck are red and 26 are black.The cards have one of four denominations: 13 cards are hearts (red),13 cards are diamonds (red),13 cards are clubs (black),and 13 cards are spades (black).Two cards are selected at random and the denomination is recorded.The event D is defined as the event that the first card is diamonds and the second card is red.Which of the following correctly defines event D^C?

A)D^C = {(diamonds,clubs), (diamonds,spades)}
B)D^C = {(hearts,clubs), (hearts,spades)}
C)D^C = {(hearts,clubs), (hearts,spades), (spades,clubs), (spades,spades), (clubs,clubs), (clubs,spades)}
D)None of the above

Question 31

The United States has 10 federal holidays.Each holiday and the date of the holiday in 2016 are listed in the table below. Suppose you work for a private company that does not observe all the federal holidays.What is the sample space for the number of federal holidays that your company might observe?

A)S = {0,1,2,3,4,5,6,7,8,9,10}
B)S = {Jan,Feb,May,Jul,Sept,Oct,Nov,Dec}
C)S = {0}
D)S = {10}

Question 32

A valid probability is either 0 or 1.

Question 33

Suppose you have a perfectly fair 10-sided die,with sample space S = {1,2,3,4,5,6,7,8,9,10}.What is the event H,which is defined as any even-numbered roll?

A)H = {1,2,3,4,5}
B)H = {1,2,3,4,5,6,7,8,9,10}
C)H = {2,4,6,8,10}
D)H = {0 or 1}

Question 34

A coin is tossed,and then a six-sided die is rolled.Which of the following defines the sample space S?

A)S = {H,T}
B)S = {1,2,3,4,5,6}
C)S = {H,T,1,2,3,4,5,6}
D)S = {H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6}

Question 35

Suppose you have a perfectly fair 10-sided die,with sample space S = {1,2,3,4,5,6,7,8,9,10}.Now suppose that the 10-sided die is rolled twice in a row.What is the probability of rolling a 9 on the second roll if a 9 was rolled on the first roll?

A)9/10
B)0
C)1/9
D)1/10

Question 36

A standard deck of cards has 52 cards.The cards have one of two colors: 26 cards in the deck are red and 26 are black.The cards have one of four denominations: 13 cards are hearts (red),13 cards are diamonds (red),13 cards are clubs (black),and 13 cards are spades (black).Two cards are selected at random and the color is recorded.Which of the following is the correct sample space S for the set of possible outcomes?

A)S = {red,black}
B)S = {(red,red), (red,black), (black,red), (black,black)}
C)S = {0,1,2}
D)S = {red,black,hearts,diamonds,clubs,spades}

Question 37

Suppose Team A has a 0.75 probability to win their next game and Team B has a 0.85 probability to win their next game.Assume these events are independent.What is the probability that Team A wins and Team B loses?

A)0.90
B)0.75
C)0.15
D)0.1125

Question 38

The second letter of a word in a text message is independent of the first letter of that word.

Question 39

The United States has 10 federal holidays.Each holiday and the date of the holiday in 2016 are listed in the table below. What is the sample space for the number of federal holidays?

A)S = {0,1,2,3,4,5,6,7,8,9,10}
B)S = {Jan,Feb,May,Jul,Sept,Oct,Nov,Dec}
C)S = {0}
D)S = {10}

Question 40

Suppose that at the Apple iPhone manufacturing plant phones are found to be defective at a rate of 1 per 100.What is the probability that you and your roommate both order iPhones and both receive defective merchandise?

A)0.1
B)0.0001
C)0.01
D)This can't be determined until the first phone is inspected.

Question 41

A valid probability is any number between -1 and 1.

Question 42

A study was conducted in a large population of adults concerning eyeglasses for correcting reading vision.Based on an examination by a qualified professional,the individuals were judged as to whether or not they needed to wear glasses for reading.In addition it was determined whether or not they were currently using glasses for reading.The following table provides the proportions found in the study. What is the probability that a selected adult is judged to need eyeglasses but does not use them for reading?

A)0.42
B)0.18
C)0.54
D)0.60
E)0.36

Question 43

Ignoring twins and other multiple births,assume babies born at a hospital are independent events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5.Define event B = {at least one of the next two babies is a boy}.What is the probability of the complement of event B?

A)0.125
B)0.250
C)0.375
D)0.500

Question 44

Suppose that A and B are two independent events.The probability that event A occurs is P(A)= 0.4 and that B occurs is P(B)= 0.2.What is the probability that A does not occur and that B also does not occur?

A)0.92
B)0.40
C)0.60
D)0.08
E)0.48

Question 45

A study was conducted in a large population of adults concerning eyeglasses for correcting reading vision.Based on an examination by a qualified professional,the individuals were judged as to whether or not they needed to wear glasses for reading.In addition it was determined whether or not they were currently using glasses for reading.The following table provides the proportions found in the study. Suppose two adults are selected from the population independently and at random.What is the probability that both were judged to need eyeglasses and neither was using them for reading?

A)0.36
B)0.1296
C)0.0324
D)0.9216
E)0.18

Question 46

A study was conducted in a large population of adults concerning eyeglasses for correcting reading vision.Based on an examination by a qualified professional,the individuals were judged as to whether or not they needed to wear glasses for reading.In addition it was determined whether or not they were currently using glasses for reading.The following table provides the proportions found in the study. If a single adult is selected at random from this large population,what is the probability that the adult is judged to need eyeglasses for reading?

A)0.46
B)0.42
C)0.78
D)0.60
E)0.40

Question 47

If you draw an M&M candy at random from a bag of the candies,the candy you draw will have one of six colors.The probability of drawing each color depends on the proportion of each color among all candies made.Assume the table below gives the probabilities for the color of a randomly chosen M&M. What is the probability of not drawing a red candy?

A)0.3
B)0.6
C)0.7
D)0.9

Question 48

At the end of a production run manufacturing rubber gaskets,items are sampled at random and inspected to determine if the item is acceptable (A)or defective (D).Suppose it is planned to select two items and determine if each is either A or D.Which set of outcomes describes the event that at least one of the items selected is defective?

A){AA,AD,DD}
B){AD,DA,DD}
C){DD}
D){AA,AD,DA}
E){AA,DD}

Question 49

Suppose a fair coin is flipped twice and the number of heads is counted.Which of the following is a valid probability model for the number of heads observed in two flips?

A)
B)
C)
D)None of the above

Question 50

Belgium has two official languages: French and Dutch.Assume that about 60% of the people speak Dutch and 40% of the people speak French.Define the event A as the event that two randomly selected Belgians speak the same language.What is the complement of event A?

A)0.48
B)0.52
C){Dutch,French}
D){(Dutch,French), (French,Dutch)}

Question 51

A standard deck of cards has 52 cards.The cards have one of two colors: 26 cards in the deck are red and 26 are black.The cards have one of four denominations: 13 cards are hearts (red),13 cards are diamonds (red),13 cards are clubs (black),and 13 cards are spades (black).Two cards are selected at random.Event C is defined as the event that the first card is clubs,event R as the event that the first card is red,and event B as the event that the second card is black.Which events are disjoint?

A)R and B only
B)R and C only
C)R and B and R and C,but not B and C
D)None of the events are disjoint.

Question 52

If you draw an M&M candy at random from a bag of the candies,the candy you draw will have one of six colors.The probability of drawing each color depends on the proportion of each color among all candies made.Assume the table below gives the probabilities for the color of a randomly chosen M&M. What is the probability of drawing a yellow candy?

A)0.1
B)0.2
C)0.3
D)This is impossible to determine from the information given.

Question 53

Ignoring twins and other multiple births,assume babies born at a hospital are independent events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5.Define events A = {the next two babies are boys} and B = {at least one of the next two babies is a boy}.What do we know about events A and B?

A)They are disjoint.
B)They are complements.
C)They are independent.
D)None of the above

Question 54

If you draw an M&M candy at random from a bag of the candies,the candy you draw will have one of six colors.The probability of drawing each color depends on the proportion of each color among all candies made.Assume the table below gives the probabilities for the color of a randomly chosen M&M. What is the probability that you draw neither a brown nor a green candy?

A)0.3
B)0.6
C)0.7
D)0.9

Question 55

In a probability model,all possible outcomes together must have a probability of 1.

Question 56

Ignoring twins and other multiple births,assume babies born at a hospital are independent events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5.What is the probability that the next three babies are of the same sex?

A)0.125
B)0.250
C)0.375
D)0.500

Question 57

If you draw an M&M candy at random from a bag of the candies,the candy you draw will have one of six colors.The probability of drawing each color depends on the proportion of each color among all candies made.Assume the table below gives the probabilities for the color of a randomly chosen M&M. If you select two M&M's and the colors are independent,then what is the probability that both are the same color?

A)0.01
B)0.09
C)0.22
D)0.25

Question 58

At the end of a production run manufacturing rubber gaskets,items are sampled at random and inspected to determine if the item is acceptable (A)or defective (D).Suppose it is planned to select two items and determine if each is either A or D.What is the sample space S of the outcomes?

A)S = {A or D}
B)S = {AA,DD}
C)S = {AA,AD,DA,DD}
D)This depends upon the assignment of probability to the outcomes of the sampling.
E)This can't be determined until the sample of two items has been collected.

Question 59

Ignoring twins and other multiple births,assume babies born at a hospital are independent events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5.What is the probability that at least one of the next three babies is a boy?

A)0.125
B)0.333
C)0.750
D)0.875

Question 60

Suppose we roll a red die and a green die.Let R be the event that the number of spots showing on the red die is three or less,and G be the event that the number of spots showing on the green die is more than three.The events R and G are _________.

A)disjoint
B)complements
C)independent
D)reciprocals

Question 61

In the United States the month of April generally has the highest amount of rainfall.Suppose the amount of rainfall from 2000 to 2013 was recorded.The amount of rainfall that fell in the month of April of each of these years is an example of a _______.

A)discrete random variable
B)continuous random variable

Question 62

What is the sample space for the number of text messages the average teenager sends per month?

Question 63

Students in a basic statistics class are allowed to take as much time as needed on their final exam.The exact amount of time it takes each student to finish the final exam is an example of a _________.

A)discrete random variable
B)continuous random variable

Question 64

On the first day of class,a professor asks each student what country they are from originally.What is the sample space?

Question 65

Suppose you have two math classes (math 1 and math 2)and two sciences courses (science 1 and science 2)that you must complete before your sophomore year in college.Assume your college is on a semester system and there are two semesters in each year.What is the sample space for the number of required math classes you take during your freshman year?

A)S = {math 1,math 2}
B)S = {0,1,2}
C)S =
D)None of the above

Question 66

You decide to visit the health center to be tested for HIV,the virus that causes AIDS.What is the sample space that represents your possible result?

Question 67

Probability distributions can be visualized graphically using a _______ for continuous random variables.

A)probability histogram
B)density curve
C)Q-Q plot
D)scatterplot

Question 68

Two events are considered independent if the outcome of one does not influence the outcome of the other.

Question 69

What is the sample space for the number of hours per week the average teenager spends on the Internet?

Question 70

The Dallas Cowboys are a team that is part of the National Football League.What is the sample space for the outcome of their next game against the Green Bay Packers?

Question 71

If two events have no outcomes in common,then those two events are ________.

A)independent
B)disjoint

Question 72

If S is a sample space,then P(S)= ___.

A)1
B)0
C).5

Question 73

Thirty random students are selected and asked questions about their favorite type of car.All the colors of their favorite car are an example of a discrete random variable.

Question 74

Suppose you have two math classes (math 1 and math 2)and two sciences courses (science 1 and science 2)that you must complete before your sophomore year in college.Assume your college is on a semester system and there are two semesters in each year.Suppose during your freshman year you can only take all math classes or all science classes.What is the event A of classes you take your freshman year?

A)A = {math 1,math 2,math 1 and math 2,science 1,science 2,science 1 and science 2}
B)A = {math 1 and science 1,math 2 and science 2}
C)A = {0,1,2,3,4}
D)None of the above

Question 75

Suppose you have two math classes (math 1 and math 2)and two sciences courses (science 1 and science 2)that you must complete before your sophomore year in college.Assume your college is on a semester system and there are two semesters in each year.Suppose you are required to take at least one of the science courses during your freshman year.What is the event A of required science courses you could take the first semester of your freshman year?

A)A = {math 1,math 2,science 1,science 2}
B)A = {science 1,science 2,science 1 and science 2}
C)A = {1}
D)A = {1,2}

Question 76

On a college campus in the northeast there are approximately 3000 students.On average there are approximately 50 classes being offered simultaneously on a given day.The number of registered students who are absent from the class is an example of a _______.

A)discrete random variable
B)continuous random variable

Question 77

A probability histogram can only be used for continuous random variables.

Question 78

Probability distributions can be visualized graphically using a _______ for discrete random variables.

A)probability histogram
B)density curve
C)Q-Q plot
D)scatterplot

Question 79

Suppose you have two math classes (math 1 and math 2)and two sciences courses (science 1 and science 2)that you must complete before your sophomore year in college.Assume your college is on a semester system and there are two semesters in each year.Suppose you are required to take exactly one of the science courses and exactly one of the math courses during your sophomore year.What is the event A of required math and science courses you could take the first semester of your sophomore year?

A)A = {math 1,math 2,science 1,science 2}
B)A = {math 1 and science 1,math 1 and science 2,math 2 and science 1,math 2 and science 2}
C)A = {1,1}
D)A = {1,2}

Question 80

Suppose you have two math classes (math 1 and math 2)and two sciences courses (science 1 and science 2)that you must complete before your sophomore year in college.Assume your college is on a semester system and there are two semesters in each year.Suppose you are only allowed to take one of the required courses during the first semester of your freshman year.What is the sample space for the course you take?

A)S = {math 1,math 2,science 1,science 2}
B)S = {0,1}
C)S = {1}
D)S = {math 1 and math 2,science 1 and science 2}