Question 1

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

Accepted Answer

The sample space is the set of possible outcomes. In this case, the possible outcomes are the number of federal holidays you take off, which can be 0, 1, 2, or 3. Therefore, the sample space is S = {0,1,2,3}. Choice B is incorrect because it only includes one possible outcome (taking all 3 holidays off). Choice C lists all of the federal holidays but does not give the sample space. Choice D is incorrect because there is a clear sample space of possible outcomes.

Question 2

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

Accepted Answer

A perfectly fair die has each outcome equally likely, meaning each outcome has a probability of 1/10. Therefore, all probabilities are equal, and the answer is B.

Question 3

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

Accepted Answer

The answer of The United States has 10 federal holidays.Each...

Question 4

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

Accepted Answer

The answer of Suppose Team A has a 0.75 probability...

Question 5

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}

Accepted Answer

The answer of The United States has 10 federal holidays.Each...

Question 6

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

Accepted Answer

The probability that both events occur is equal to the product of their individual probabilities because the events are independent. Therefore, the probability that both Team A and Team B win is 0.75 x 0.85 = 0.6375.

Question 7

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}

Accepted Answer

The sample space S should represent all possible outcomes of selecting a card in terms of its denomination. Therefore, option A is incorrect as it only considers the color. Option B is incorrect as it lists duplicate outcomes. Option D is incorrect as it combines both color and denomination which may lead to confusion. Option C is correct as it lists all four possible denominations in the deck.

Question 8

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

Accepted Answer

The answer of Which of the following define a complete...

Question 9

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)}

Accepted Answer

Event H is defined as the event that the first card is hearts, which means the second card can be any denomination, including hearts again. Therefore, all combinations where the first card is hearts are included.

Question 10

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

Accepted Answer

Event D specifies the first card is diamonds and the second card is red. None of the options correctly represent this event, as they either don't include a diamond as the first card or include non-red cards as the second card.

Question 11

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}

Accepted Answer

The sample space represents all possible outcomes of an experiment. In this case, the experiment is whether or not the private company observes each of the 10 federal holidays. Therefore, the sample space includes all possible numbers of federal holidays that the company might observe, which includes observing none, some, or all of the holidays. The set of integers from 0 to 10 includes all of the possible values, so choice A is the best answer.

Question 12

A valid probability is either 0 or 1.

Accepted Answer

A probability can range from 0 (impossible) to 1 (certain), but it can also have values between 0 and 1, indicating varying degrees of likelihood.

Question 13

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}

Accepted Answer

The event H includes any even-numbered roll, which is {2,4,6,8,10}. Therefore, the correct choice is C. Option A is incorrect because it includes odd numbers. Option B is also incorrect because it includes all numbers in the sample space, including odd numbers. Option D is incorrect because the die only has 10 sides, so it is not possible to roll a 0 or 1.

Question 14

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}

Accepted Answer

The sample space should include all possible outcomes of both the coin toss and the die roll. Since the coin can land as heads (H) or tails (T) and the die can land on any number from 1 to 6, the combined outcomes are represented as H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6.

Question 15

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

Accepted Answer

The outcome of the second roll is independent of the outcome of the first roll. Therefore, the probability of rolling a 9 on the second roll remains 1/10, regardless of the first roll's outcome.

Question 16

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}

Accepted Answer

The sample space consists of all possible outcomes when two cards are selected at random. Each outcome is represented by a pair of colors (red or black) chosen without replacement. Therefore, the correct sample space is {(red,red), (red,black), (black,red), (black,black)}. Option A only lists the possible colors and not the pairs, Option C and D are incorrect because they include outcomes that are not possible (i.e. selecting 0 or 1 cards, or specifying a suit instead of a color).

Question 17

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

Accepted Answer

The probability that Team A wins is 0.75 and the probability that Team B loses is (1-0.85) = 0.15. Since these events are independent, we can multiply their probabilities to get the probability that both events happen at the same time: 0.75 x 0.15 = 0.1125. Therefore, the answer is D.

Question 18

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

Accepted Answer

The second letter of a word is often dependent on the first letter due to the rules of phonetics, spelling, and the structure of the language, which influence how letters can be combined to form words.

Question 19

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}

Accepted Answer

The sample space would be the set of possible values for the number of federal holidays, which is simply the set {0,1,2,3,4,5,6,7,8,9,10}. Therefore, the answer is choice D.

Question 20

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.

Accepted Answer

The probability of one phone being defective is 1/100, so the probability of both phones being defective is (1/100) * (1/100) = 0.0001.

Quiz 4: Probability: the Study of Randomness

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?

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?

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?

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?

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?

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

A valid probability is either 0 or 1.

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

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?

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?

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

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?

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?