AQR A Final

A standard deck of playing cards contains 52 cards in total, four of which are Queens. Martina the magician calls up two volunteers, Lexie and Dustin. Both Lexie and Dustin choose a card without looking and hold it behind their backs, so Martina the magician cannot see them. Martina the magician correctly guessed that both volunteers had chosen a Queen! Which of these expressions gives the probability that both volunteers chose a Queen? Are these dependent or independent events?

( 4/52 ) ( 3/51 ) dependent

Over his career, Michael Jordan had a 0.497 field goal percentage, meaning his probability of making a typical shot was 49.7%. If each shot was independent of the others, what would be the probability him missing 5 shots in a row?

(1 - 0.497)^5

Which of these best describes the probability of flipping a coin four times and never getting any of the flips to land on heads?

(1/2)^4 ; independent events

Suppose an athlete is training for an event which includes running and swimming. The probability that he beats his personal record for the running event is 0.35, the probability of beating his swimming record is only 0.11, and the probability that he beats both records at the same event is 0.08. During the event, if he already breaks his running record, then what is the probability that he breaks his swimming record?

0.23

Joellen purchased three types of cookies and puts them all into one box in her cupboard. 100 cookies contain chocolate chips but no peanuts. 75 cookies contain peanuts but no chocolate chips. 50 cookies contain chocolate chips and peanuts. At night when the house is dark, Joellen removes a cookie from the box. When she eats it, she discovers that it has chocolate chips. What is the probability that it also has peanuts?

0.33

If 91% of all teenagers use the internet, and 57% of online teens have a picture on a social networking site, then what percentage of all teenagers are online and have NOT posted a picture on a social networking site?

0.39

A baseball player has the following statistics: singles = 42 doubles = 28 triples = 11 home runs = 15 total times at bat: 325 Determine the slugging average based on these statistics.

0.588

A high school offers the following math courses: Algebra 1, Geometry, Algebra 2, Pre-Calculus, AP Statistics, and AP Calculus. If you randomly selected one of these math courses, what is the probability that you do NOT select an AP course?

0.67

The probability that an expert archer hits their mark is 0.94. If each shot taken is independent, then what is the probability that the archer hits 5 consecutive marks?

0.73

State the number of significant digits each of the following has. 1. 427.01 2. 0.00052 3. 2301.0 4. 320,000 5. 2.75 x 104

1. 5 2. 2 3. 5 4. 2 5. 3

For a graph with seven edges, what is the sum of its degrees?

14

A movie with an aspect ratio of 2.25:1 is shown on a 46" television. What is the height of the image? Round to the hundredths.

17.78

Which of the following combination of degrees (vertices) for a graph is not possible?

2, 3, 4, 4

What is the height of the black border at the top and bottom for a movie with an aspect ratio of 2.25:1 when shown on a 46" television?

2.61"

Twenty-four students are registered for summer school courses at Kensington Green High School. The Algebra 2 class has 8 students and the Biology class has 12 students and 3 students are in Algebra 2 and Biology. If one of the summer school students was selected at random, what is the probability that the student is not in Biology and not in Algebra 2?

29%

An elevator has about 90 square feet of space. The average person needs 2.5 square feet of space. If the average person weighs 150 pounds and the elevator is full, about how much weight is the elevator supporting?

5,400 pounds

If the sum of the degrees for a graph is 16, how many edges does the graph have?

8

A grocery chain surveyed 200 customers and found the following facts. 160 customers purchased vegetables. Only 80 customers were male. 70 customers were male and purchased vegetables. How many females purchased vegetables? What is the grocery chain's best estimate for the percentage of their customers who are female and purchase vegetables?

90, 45%

Twenty-two students are registered for summer school courses at Kensington Green High School. The Algebra 2 course has 11 students The Biology course has 10 students 4 students are in Algebra 2 and Biology. An unknown number of students are in other courses. Which of these describes how the principal may calculate the probability that a randomly selected student is in neither Algebra 2 nor Biology?

Count the total number of students in Algebra or in Biology = 11 + 10 - 4 = 17. Subtract this number from 22 to find the number of students in neither course. 22 - 17 = 5. Divide this by the total number of students. 5/22 = 0.227.

Suppose P(B/A) = P(B), and P(A/B) = P(A). What can we say about events A and B?

Events A and B are independent

Suppose there are two carnival games. Game 1: Grab a ring out of the water without looking. If the ring has an even number, you get to throw a dart. If the ring is an odd number, you win a small prize. The rings are numbered from 1 to 20. At the dart game, the operator tells you there is a 1 in 4 chance you will win a large prize, otherwise you win nothing. Game 2: Spin a wheel with 4 colors of equal likelihood. Then pick a ring out of a bag without looking. The bag contains an equal number of rings with colors that match the colors on the wheel. If the color you spin matches the color you pull out of the bag, you win a large prize. Suppose that each game costs $4 to play. To you, the large prizes are worth about $10 and the small prizes are worth $1. Use expected value to decide which game is a better value for you.

Game 2 is better because you expect to lose only about $1.50 per game.

. Which of the following must be true? I. Mutually exclusive events cannot happen at the same time. II. When events are independent, the first event does not affect the probability of the second event. III. The probability of an event cannot be larger than 100%.

I, II, and III

Which of these is an example of a compound conditional statement? I. If there is music, then I will go to the party. II. If a triangle has two or three congruent segments, then it is isosceles.

II only

Imagine you have $1000 to invest. Your financial adviser says you have two options to invest in. Stock 1: High risk, high reward 15% chance that your money will double in the next year ($1,000 gain) 85% chance that your money will grow by the rate of inflation ($40 gain). Stock 2: Low risk, low reward. 80% chance of growing by $200 10% chance that it will grow by about $125 10% chance that it will grow at the rate of inflation ($40 gain). Use the given information and expected value to make the best choice.

Invest in stock 1 because the expected value is larger. Stock 1: The expected value is (0.15)(1,000) + (0.85)(40) Stock 2: The expected value is (0.8)(200) + (0.1)(125) + (0.1)(40)

9. Try to imagine a connected graph with two vertices and one of the vertices has a degree of 1 and the other vertex has a degree of 2. Is this possible? Why or why not?

No, because this graph would have two edges which means the sum of the degrees must be four, not 3.

Which of the statements below uses the condition that event A already occurred?

P(B | A)

A grocery chain surveyed 200 customers and found the following facts. 160 customers purchased vegetables. Only 80 customers were male. 70 customers were male and purchased vegetables. Let event X = male and event Y = bought vegetables. Which of these represents the probability that a randomly selected customer is male or purchased vegetables?LaTeX: \times

P(X) + P(Y) - P(X and Y)

An online retail store surveyed 200 customers and found the following facts. 132 customers purchased clothing. 75 customers live outside of the United States. 70 customers live in the United States and purchased clothing. Let event X = lives in the United States and event Y = bought clothing. Which of these represents the probability that a randomly selected customer lives in the United States or bought clothing?

P(X) + P(Y) - P(X and Y)

Which of the following describes if the graph has a Euler path or circuit?

The graph has a path because there are exactly 2 odd vertices.

Determine the inflation rate by comparing the CPI from the year 2000, when CPI=172.200, to the CPI of 2016, which is 240.008.

The inflation rate is 39.4%.

Which of the following represents the meaning of the price index below? Price index today versus the year 2000: 71%

The price today is about 71% of the price in 2000.

Which of these is the best interpretation of the formula P(A/B) = P(A and B) / P(B)

The probability that event A happens, given that event B happens is found by dividing the probability that both A and B happen together, divided by the probability of event B.

A gym scales measures your weight to be 137.20 pounds. Which of the following describes the accuracy of this weight?

The scale is accurate to the nearest hundredth of a pound.

Which of these statements must be true? There are 6 vertices so there must be 6 edges. There are 6 edges so the degree of each vertex must add up to 6. There are 6 vertices so there must be 12 edges. There are 6 edges so the degree of each vertex must add up to 12.

There are 6 edges so the degree of each vertex must add up to 12.

Stanley runs a produce market which sells fruits, vegetables, and some bakery items. He knows that for every 100 customers, 42 buy fruits, 57 buy vegetables, and 25 customers buy both. Stanley wishes to find out how many customers do not buy fruits or vegetables. Which of these best describes how to set up a Venn Diagram to represent the situation?

Write 25 in the intersection. Subtract 42 - 25 and write 17 in the part of the circle representing customers that buy only fruits. Subtract 57 - 25 and write 32 in the part of the circle representing customers that buy only vegetables. Subtract the sum of these numbers from 100 to find the answer.

Rank these outcomes from least likely to most likely when rolling a pair of dice. X = rolling a 3 Y = rolling a 6 Z = rolling a 12

Z, X, Y

Hamilton paths and circuits must go through every _______ exactly one time.

vertex

Reference the same airplane problem from above and find the missing angle measures in the triangle.

x=30.9; y=74.1

A baseball has the following statistics after 285 times at bat: singles: 23 doubles: 15 triples: 7 home runs: 5 What is the batter's average?

0.330

Justamere High School currently has 74 classrooms in session and three of which are elective courses like computer programming or wood shop. If Mrs. Rosie Soto randomly selects a course to observe, what is the probability that she picks a non-elective course?

0.96

A 4 digit combination for an alarm code has the following restrictions: the first digit cannot be 0 the second digit must be odd the 3rd digit must be a multiple of 3 the 4th digit can be any number 0 to 9. How many combinations are possible?

1,350

Given that p = false and q = true, determine the truth value of each. i) LaTeX: p\vee q p ∨ q ii) LaTeX: p\wedge q p ∧ q iii) LaTeX: p\longrightarrow q p ⟶ q

1. true 2. false 3. true

Given that p = true and q = true, determine the truth value of each. i) LaTeX: p\vee q p ∨ q ii) LaTeX: p\wedge q p ∧ q iii) LaTeX: \sim q ∼ q

1. true 2. true 3. false

A group of friends is playing a game where players take turns drawing a marble from a bag, like the one pictured below. The bag contains 3 white marbles, 4 gray marbles, and 5 black marbles. If a player draws a white marble, they have to answer a trivia question. If a player draws a black marble they win a prize. If a player draws a gray marble, the player loses his or her turn. Players do not replace their marble before the next player chooses a marble from the bag. What is the probability that player 3 loses his or her turn given that the first two players did not lose their turn?

2/5

Consider the following statistics. 71% of American teenagers own a cell phone. 57% of American teens have at least one picture on a social networking site. What percentage of American teens own a cell phone and have not posted a picture on a social networking site?

31%

A password for your tablet login is a 5 digit code with the following restrictions: The first number cannot be 0 or 9 The second number must be even The third number must be odd The fourth number is between 2 and 8, inclusively The last digit is a multiple of 4 How many combinations are possible?

4,200

Miranda is playing a lottery game where he selects a marble out of bag and then replaces it after each pick. There are 6 blue marbles and 9 red marbles. With replacement, what is the probability that George will draw two blue marbles in two tries to win the lottery?

4/25

A television screen measures 46" (on the diagonal) with an aspect ratio of 16:9. What are the dimensions of the television screen? Round to the nearest whole number.

40" by 23"

An online retail store surveyed 200 customers and found the following facts. 132 customers purchased clothing. 75 customers live outside of the United States. 70 customers live in the United States and purchased clothing. How many customers live in the United States but did not buy clothes? What is the online retailer's best estimate for the percentage of their customers who live in the United States but do not purchase clothing?

55, 28%

A combination locker uses a three number combination. Each number in the code must be from 00 to 39 inclusive, however no number can be repeated in the combination. For example, the combination 00-39-12 is valid, but the combination 00-12-00 is not valid. How many different combinations can there be?

59,280

An airplane travels at a rate of 375.0 mph for 2.000 hours and is then thrown off course due to a storm. The plane travels for another hour at a rate of 400.0 mph. What is the distance of the plane from the airport after 3.00 hours of travel? Give answer to 4 significant figures.

753.1 miles

What percent of the screen is utilized if a movie with an aspect ratio of 2.25:1 is shown on a 46" television screen?

77%

Imagine you have $1000 to invest. Your financial advisor says you have two options to invest in. Stock 1: High risk, high reward Stock 2: Low risk, low reward She estimates that stock 1 gives you approximately a 10% chance that your money will double in the next year ( $1,000 gain) and there is approximately a 90% chance that your money will grow by the rate of inflation ($40). She estimates that stock 2 has a 90% chance of growing by $200 and a 10% chance that it will grow by about $125. Which of these describes the expected value of these two stocks?

C. Stock 1 expects to earn $136 in a year. Stock 2 expects to earn $192.50 per year.

. Rank these outcomes from least likely to most likely when rolling a pair of dice. X = rolling a 6 Y = rolling a 9 Z = rolling a 12

Z, Y, X

Which of the following methods would produce an accurate estimate to the following question? How much does it cost in vet bills over the course of a dog's life?

average vet bill x # of visits per year x average lifespan for a dog

Andrew surveyed students at his school. He found that 67 students own a cell phone and 48 of those students own a portable gaming device. There are 13 students that do not own a cell phone, but own a portable gaming device. Nine students do not own either device. Identify the two variables.

cell phone and gaming device

Euler paths and circuits must go through every ______ exactly one time.

edge

David took a survey at his school to determine which students knew how to swim. He found that in the 6th grade, 120 could swim, 60 could not; in the 7th grade, 168 could swim, 11 could not; in the 8th grade, 172 could swim, 3 could not. Identify the two variables.

grade level and swimming ability