algebra 2b - unit 4: theoretically speaking lesson 16-20

the probability of event n^c occurring in an experiment is p(n^c) = 0.85. what is p(n)?

0.15

the probability of event a occurring in an experiment is p(a) = 0.62. what is p(a^c)?

0.38

the probability of event b^c occurring in an experiment is p(b^c) = 0.47. what is p(b)?

0.53

alex is rolling a typical six-sided die. what is p({x : x is not a prime number})?

1/2

based on the experimental probability, what are the chances that the next spin will result in a number less than 5?

1/2

abe is going to roll a fair standard six-sided die. what is p({x : x is not less than 5})?

1/3

based on the experimental probability, what are the chances that this week's quiz will be tomorrow?

1/3

based on these results, what is the probability that the next jelly bean brianna draws out of the bag will be purple?

1/3

what is the probability that the dance will be held in the middle of the month (any day from the 11th through the 20th date of the month)?

1/3

what is the value of p(x : x is a red section)?

1/3

what is the experimental probability of winning, according to sammy's observations?

1/30

what is the probability that eloise will win the game if she randomly pulls two slips of paper from the bag?

1/35

if demetra spins the wheel one time, what is the probability of spinning the green section?

1/4

what is p({x : x is a multiple of 4})?

1/4

what is the probability that jacob will win the game after rolling the die once and spinning the spinner once?

1/4

wendy is drawing a single card at random from a standard deck of 52 cards. if there are 12 face cards in the deck, what is p({x : x is not a face card})?

10/13

yesenia is working with the following spinner. what is the experimental probability that her next spin will be a 4?

11/20

what is the probability that the next marble alejandro draws will be orange based on the experimental data?

11/49

what is the sum of 1/4 and 2/5 when written in simplest form?

13/20

what is rico's experimental probability of seeing a red car?

13/30

wes is about to roll a standard six-sided die. what is p({x : x is not divisible by 3})?

2/3

what is the probability that kegan selects a cup that does not contain the ball underneath it?

2/3

based on these results, what is the probability that the next jelly bean jose draws out of the bag will be green?

2/5

what is angelica's experimental probability that a fish will pass that is not a bluefin tuna?

2/5

the probability of event a^c occurring in an experiment is p(a^c) = 73/100. what is p(a)?

27/100

based on these results, what is the probability that the next jelly bean toros draws out of the bag will be yellow?

3/20

steve is preparing to draw a single card from a standard deck of 52 cards. what is the probability that steve does not draw a spade?

3/4

reduce the fraction 72/120

3/5

what is the probability that amelie spins either an odd number or a red number?

4/5

the probability of event a occurring in an experiment is p(a) = 4/9. what is p(a^c)?

5/9

lauren checks the weather forecast and sees that there is a 44% chance of snow today. what is the probability that it will not snow today, as a percentage?

56

lily checks the weather forecast and sees that there is a 35% chance of rain today. what is the probability that it will not rain today, as a percentage?

65

what is the probability that amelie spins an odd number or a green number?

7/10

the probability of event a occurring in an experiment is p(a) = 27/35. what is p(a^c)?

8/35

elizabeth has the following spinner, where the spaces are of equal size and are numbered 1 through 10. what is p(a∩b)?

9/100

in an experiment with sample space s, there are four events: a, b, c, and d. the theoretical probabilities for each are p(a) = 5/11, p(b) = 4/11, p(c) = 6/11, and p(d) = 8/11. which two events might be complementary?

a and c

in an experiment with sample space s, there are four events: a, b, c, and d. the theoretical probabilities for each are p(a) = 1/3, p(b) = 1/2, p(c) = 3/4, and p(d) = 2/3. which two events might be complementary?

a and d

examine the following data, which shows the approximate height, in feet, of a stuntman jumping from a building onto an airbag. mark wants to simulate this motion to make some predictions for a movie production. which type of model is most consistent with the actual data set shown in the graph?

a quadratic model

two simulations are described below. which type of data, if any, is recorded for each? match each simulation with the type of data that is recorded, if any, for that simulation.

a six-sided die with sides of the colors purple, green, red, yellow, orange, and blue is rolled, and the results are recorded : this stimulation records categorical data a standard six-sided die (with sides labeled 1 through 6) is rolled, and the results are recorded : this stimulation records numerical data

two simulations are described below. which type of data is recorded for each, if any? match each of the two simulations with the type of data, if any, that is recorded for that simulation.

a spinner labeled 1-10 is spun, and the results are recorded : this simulation records numerical data. a spinner landed with the colors red, green, orange, and blue is spun, and the results are recorded : this stimulation records categorical data

two simulations are described below. which type of data is recorded for each, if any?

a survey question about popular social media is evaluated by random participants : this simulation records categorical data. an exponential function is evaluated for random input values : this simulation records numerical data.

part a: what is the correlation coefficient for a linear regression model of this data? part b: what is the coefficient of determination for a quadratic regression model of this data?

a: -0.93 b: 0.88

suppose the chance of a hurricane hitting the east coast this month is 37% part a: what is the complementary event in this situation? part b: what is the probability that the complementary event will occur?

a: a hurricane not hitting the east coast b: 63%

a: is a linear model a good fit for this data set? b: is a quadratic model a good fit for this data set?

a: a linear model is a good fit for this data set because the correlation coefficient is close to -1. b: a quadratic model is a good fit for this data set because the coefficient of determination is greater than 0.8.

suppose the chance of alejandro visiting south africa in his lifetime is 16%. part a: what is the complementary event in this situation? part b: what is the probability that the complementary event will occur?

a: alejandro not visiting south africa b: 94%

alexis is playing a game in which she must roll a die twice. part a: what type of compound events are k and l? part b: what is the probability of rolling two odd numbers in this game?

a: independent b: 1/4

examine the following table, which shows a subset of values from the function f(x). then, answer part a and part b. part a: which function family does f(x) belong to? part b: the function family can be identified because the _[blank]_ remains constant.

a: linear b: rate of change

use the following graph of function f(x) to answer the questions. part a: which function family does f(x) belong to? part b: which phrase justifies the correct answer to part a?

a: logarithmic b: f(x) has a vertical asymptote, and f(x) increases less and less rapidly as x increases.

suppose the chance of getting bitten by a radioactive spider on a field trip is 1%. part a: what is the complementary event in this situation? part b: what is the probability that the complementary event will occur?

a: not getting bitten by a radioactive spider b: 99%

suppose the chance of winning a raffle is 11%. part a: what is the complementary event in this situation? part b: what is the probability that the complementary event will occur?

a: not winning the raffle b: 89%

in an experiment with sample space s, there are four events: a, b, c, and d. the theoretical probabilities for each are p(a) = 5/6, p(b) = 1/4, p(c) = 6/8, and p(d) = 1/5. which two events might be complementary?

b and c

lesson 17

basic probability review

the theoretical probability of rolling a 12 is _[blank 1]_, and the experimental probability of rolling a 12 is _[blank 2]_.

blank 1: 1/12 blank 2: 20/100 = 1/5

a fair, 10-sided die with sides labeled 1 through 10 is rolled 20 times. the results are shown in the following table. the theoretical probability of rolling an even number on this die is _[blank 1]_, and the experimental probability of rolling an even number on this die _[blank 2]_.

blank 1: 1/2 blank 2: 9/20

a set of data has a correlation coefficient of −0.1 for a linear regression and a correlation of determination of 0.97 for a quadratic regression. this data is most accurately modeled by _[blank 1]_. this type of function forms a _[blank 2]_, and most of the data points will lie _[blank 3]_ it.

blank 1: a quadratic function blank 2: parabola blank 3: fairly close to

rolling an odd number and spinning an even number are examples of _[blank 1]_ events because the outcome of a die roll _[blank 2]_ affect the outcome of spinning the spinner.

blank 1: independent blank 2: does not

a theoretical probability is calculated by comparing the _[blank 1]_ to the_[blank 2]_, while an experimental probability is calculated by comparing the _[blank 3]_ to the_[blank 4]_.

blank 1: number of favorable outcomes blank 2: number of possible outcomes blank 3: number of successful trials blank 4: number of total trials

matt and david disagree about a case of probability. the two have a 20-sided die with sides labeled 1 through 20. they rolled the die 50 times. the information in the following table shows the number of times each number was rolled. who is correct? why?

both matt and david are correct. matt's probability is a theoretical probability based on the fact that there are 10 even numbers out of 20 numbers on the die. david's probability is an experimental probability based on the fact that, in the last 50 experiments, there were 30 successes (even numbers).

lesson 18

complementary events

lesson 19

compound events

what is the probability that the next two cards she is dealt are the 4 of clubs and the 6 of clubs?

dealing the next two cards is a dependent event. since sally has already been dealt 3 cards, there are 49 cards left in the deck. only 1 of those cards is the 4 of clubs, and only 1 of those cards is the 6 of clubs. therefore, sally has a 1/49(1/48) = 1/2352 chance of being dealt those two cards next.

which option describes a simulation?

dylan created a spreadsheet that randomly generates a number every time it is refreshed. he refreshed the spreadsheet 20 times and recorded the results.

if the die is rolled a total of 10,000 times, what is the most likely thing to happen?

each number should be rolled closer to the same amount of times as compared to the first 100 rolls.

jaqua collected some data and used a model to represent the data. his data and model are shown in the following graph. which model did Jaqua most likely use for his data?

exponential

use the following graph of function f(x) to answer the question. https://cdstools.flipswitch.com/asset/media/701506 which function family does f(x) belong to?

exponential

use the following graph of function f(x) to answer the question. https://cdstools.flipswitch.com/asset/media/701500 which function family does f(x) belong to?

f(x) is a quadratic function. its graph is the shape of a parabola, its domain is (−∞, ∞), and it has no vertical or horizontal asymptotes.

which graph shows data that appears to be exponential?

https://cdstools.flipswitch.com/asset/media/692726

a biologist studying a culture of bacteria wants to know how quickly it will grow. he uses a simulation to predict the growth of the bacteria. the results of the simulation are shown in the following table. which data set of actual bacteria population is he most likely trying to simulate?

https://cdstools.flipswitch.com/asset/media/692740

lina has the following sample of data points that show the percentage of the surface area of a lake that is covered in algae, given in the time, in days, that have passed since the algae was introduced into the lake. which simulation model is most consistent with the data points given in the table?

https://cdstools.flipswitch.com/asset/media/706209

james has a hat that contains 100 slips of paper, each of which has the same shape and size. which analysis of his statement is most accurate?

james may be correct, but his experimental probability of 0/20 may be misleading. he should perform more experiments to help determine whether his statement is accurate.

mr. consuelos spun the spinner 20 times and recorded the results in the following table. considering these results, which of the following students calculated an experimental probability?

jermaine calculates p({x : x is a red section}) = 7/20 natalie calculates p({x : x is a section with a number 5}) = 3/10 austin calculates p([x : x is a section with an odd number}) = 13/20

which of the answer options are examples of theoretical probability?

kaylee will roll a fair, 10-sided die with sides labeled 1 through 10. before rolling, she tries to determine the probability of rolling a multiple of 3. simon spins the spinner shown. he uses a measuring tool to determine the central angles of each sector and then calculates the probability of spinning an odd number.

maz places all of the slips of paper, which are equal in size and shape, into a bag and draws one name at random. which two events are overlapping events in this experiment?

maz draws a male's name. maz draws a blue slip of paper.

lesson 16

modeling data from stimulations

which option applies the correct formula and gives the correct answer for the probability that hastin wants to find?

p(a∪b) = p(a) + p(b) − p(a∩b) = 23/48 + 2/48 - 1/48 = 24/48 = 1/2

a fair, 20-sided die with sides labeled 1 through 20 is rolled. consider the following events, and then answer the question. which probability is the smallest?

p(b)

a bag contains 100 marbles: 30 are red, 25 are green, 15 are blue, 7 are yellow, and the rest are orange. which probability is the smallest?

p(d)

anais placed 100 slips of paper, all equally sized and shaped, into a bag. which probability is a theoretical probability?

p({x : x is a blue slip of paper}) = 3/20

each day of the week is listed on an equally sized and shaped slip of a paper. all seven slips are placed in a bag. one slip is randomly drawn. which event has the greatest probability?

p({x : x is a weekday})

john is choosing a single card at random from a standard deck of 52 cards. which option(s) represent(s) a pair of complementary events in this situation?

r = {x : x is a red card} and b = {x : x is a black card} f = {x : x is a face card} and f^c = {x : x is not a face card}

examine the following data that shows the average height of a palo verde tree. genevieve wants to simulate the growth of this tree to see if she can grow it inside of a greenhouse at the botanical garden she manages. which simulation model is most consistent with the average height of the tree?

radical model

considering this spinner, which two events are disjoint? select all that apply.

spinning a multiple of 3 spinning a purple space.

which is greater, the experimental probability of drawing an orange jelly bean or the theoretical probability of drawing an orange jelly bean?

the experimental probability is greater than the theoretical probability.

which is greater, the experimental probability of rolling a 4, or the theoretical probability of rolling a 4?

the experimental probability is greater than the theoretical probability.

which description of a graph of points is best suited to a logarithmic model?

the points appear to be close to a vertical line, then begin to cluster around a curve that steadily increases as x increases.

an engineer simulates the average miles driven by a truck, using a model that relates t, time in years, to m, the amount of miles driven by the truck. he obtains from his simulation the set of data points that appear in the following table. which simulation model is most consistent with his simulation? why?

the set of data obtained from the simulation tends to be exponential, and this set of data tends to be exponential as well.

an engineer simulates the flight of an airplane using a model that relates t, time in hours, to d, total distance traveled by the plane in miles. he obtains from his simulation the set of data points that appear in the following table. which simulation model is most consistent with his simulation? why?

the set of data obtained from the simulation tends to be linear, and this set of data tends to be linear as well.

victor examined some data from his savings account. when he compared the time in years since he started the account to the amount of savings that was in his account, he noticed a pattern. as time went by, his savings increased quickly at first, but the rate of change slowed down over time. which simulation model is most consistent with the data from victor's account? why?

the set of data obtained from the simulation tends to be logarithmic, and the pattern that victor noticed in his account tends to be logarithmic as well.

a student simulates the flight of a rocket using a model that relates tt, time, to h, height. he obtains from his simulation the set of data points that appears in the following table. which actual set of data is most consistent with his simulation? why?

the set of data obtained from the simulation tends to be quadratic, and this set of data tends to be quadratic as well.

which is greater, the experimental probability of a truck having a sponsorship decal, or the theoretical probability of a truck having a sponsorship decal?

the theoretical probability is greater than the experimental probability.

which is greater, the experimental probability of rolling a 3, or the theoretical probability of rolling a 3?

the theoretical probability is greater than the experimental probability.

which is greater, the experimental probability of spinning a 3, or the theoretical probability of spinning a 3?

the theoretical probability is greater than the experimental probability.

which is greater, the experimental probability of tails or the theoretical probability of tails?

the theoretical probability is greater than the experimental probability.

which is greater, the experimental probability of selecting a green candy, or the theoretical probability of selecting a green candy?

there is not enough information to determine which probability is greater.

if kyra draws two slips of paper, and does not replace the slip after the first draw, which description of events a and b is accurate?

they are dependent events because there are two trials and kyra does not replace the paper.

which set(s) of data could best be described by a linear model? select all that apply.

x : -2 -1 0 1 y: 5 8 11 14 AND x: -2 -1 0 1 y: -9 -19 29 -39

which set of data is most accurately represented by a logarithmic model?

x: -2, -1, 0, 1, 2 y: 0.3, 0.48, 0.6, 0.7, 0.78

which data set is most accurately described as linear?

x: -2, -1, 0, 1, 2 y: 13, 10, 7, 4, 1

consider a standard deck of 52 playing cards. if f = ({x : x is a king or jack}, and b = {x : x is a black card}, to what is the intersection f ∩ b equal?

{jack of spades, king of spades, jack of clubs, king of clubs}

consider a standard deck of 52 playing cards. if a = {x : x is a diamond card}, which event is the complement of a?

{x : x is a heart, spade, or club card}