Geometry Semester B PLE End of Semester Exam Review

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PLATO Course Geometry, Semester B v3.0 > End of Semester Test - Geometry B Review

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Question 1

The probability that Shelly will go to a movie (event A) on Friday is 0.78, and the probability that Danielle will go to a movie (event B) the same day is 0.63. The probability that Shelly will go to a movie, given that Danielle goes to a movie, is 0.87. Which statement is true?

Events A and B are independent because P(A|B)   P(A).

Events A and B are independent because P(A|B) = P(B).

Events A and B are dependent because P(A|B) = P(A)   P(B).

Events A and B are dependent because P(A|B)   P(A).

Question 2

The probability that a given sample analyzed in a pathology lab contains protein is 0.73 (event A). The probability that the sample contains the protein albumin is 0.58 (event B).The probability that a sample contains protein given that albumin is detected, is 1. Which statement is true?

Events A and B are dependent because P(A|B) = P(A).

Events A and B are dependent because P(A| B)     P(B).

Events A and B are dependent because P(A|B) = P(A) + P(B).

Events A and B are dependent because P(A| B)     P(A).

Events A and B are dependent because P(A|B) = P(A).

Question 3

Answer the question based on the data in the table.

ShirtColor

Size

Large Medium Total

Red 42 48 90

Blue 35 40 75

Total 77 88 165

Which inference can be made from the data in the two-way table?

P(shirt is red|shirt is large) = P(shirt is large)

P(shirt is medium and blue) = P(shirt is medium|shirt is blue)

P(shirt is large|shirt is red) = P(shirt is red)

P(shirt is blue|shirt is large) = P(shirt is blue)

P(shirt is medium and blue) = P(shirt is medium)

Question 4

ShirtColor

Size

Large Medium Total

Red 42 48 90

Blue 35 40 75

Total 77 88 165

If you pick a shirt at random from the given batch of total shirts, what is the probability that it is blue and the size is large? How about a blue medium? How about a red large? How about a red medium?

Question 5

If 6 cards are drawn at random from a standard deck of 52 cards, what is the probability that exactly 2 of the cards are spades?

Answer 0.315

Question 6

If 3 cards are drawn from an ordinary deck of 52 playing cards, what is the probability that each card is a face card. (There are 12 face cards in a deck.) (Answer 0.00995)

Suppose the problem in example 13 was changed to read, "What is the probability of drawing a club from a deck, and then drawing the ace of hearts (without putting the first card back)?" This is now an example of dependent events; the occurrence of the first draw

affects the second draw. When drawing the second card the total number of cards in the deck has changed. This means that the sample space is altered and the probability of getting an ace will be different than if all the cards were in the deck. The probability of drawing a club is still the same, namely

1  = 1(52 - 1) 51

So the probability of the two events occurring is

1  • 1  = 14 51 204

Question 7

There are 12 face cards in a standard deck of 52 cards. How many ways can you arrange a standard deck of 52 cards such that the first card is a face card?

Top of Form

12P1

12C1

12P1 × 51P51

12C1 × 51P51

12C1 × 51C51

Question 8

A class consists of 55% boys and 45% girls. 25% of the class are boys and scored an A on the test, and 35% of the class are girls and scored an A on the test. If a student is chosen at random and is found to be a girl, what is the probability that the student scored an A? (Answer .78)

Question 9

Ticket master has data that shows that 15% of buyers will not be satisfied with the seats they get purchase for concerts. You also know that 10% of buyers actually are not satisfied with their seats. What is the probability that a buyer actually is satisfied?

Question 10

Be able to write equation implies that A and B are independent / dependent events.

Question 11

Two dice are thrown simultaneously. Given that sum of the numbers is NOT more than 5, what is the probability that sum is more than 3?

Question 12

You have 5 Scrabble tiles with different letters of the alphabet in a bag. If you select 3 tiles, how many distinct sequences can you form if the order matters?

Question 13

Matt’s family has a history of sickle cell anemia. The probability that Matt would inherit this disease is 0.75. Kevin decides to take a test to check if he has the disease. The accuracy of this test is 0.95.

We now know that the test predicted that Matt does not have the disease. Using this information, calculate the probability that Matt does not have sickle cell anemia after the test was taken.

Question 14 (Answer 1/ 512 )

If a coin is flipped 10 times, what is the probability that it will show all heads or all tails

Question 15 ( answer is 6.4%)

Andy is getting his office painted. Andy gets to choose the paint color, but his boss has to approve it. The probability of Andy choosing red is 32%. The probability that his boss approves Andy's choice is 20%. What is the probability that Andy chooses red and his boss approves

Question 16

An experiment consists of selecting a number at random between 0 and 5 inclusive , and a letter from the English alphabet. What is the size of the sample space of this experiment?

Hint: If you have an Event E that is defined as the occurrence of one or more of two mutually exclusive events, E1 and E2 you find the probability of that event E by adding the probabilities of E1 and E2….

Question 18

The Venn diagram shows event A and event B comprised of outcomes from the same sample space. If the probability of A is .4 and the probability of neither event A nor event B is .3, then what is the probability of event B?

Question 19 ( answer 29.0%)

The probabilities of contamination in medicine capsules from the presence of heavy metals and different types of microbes are given in the table. If capsule A shows microbial contamination, what is the chance that the contamination is from Salmonella?

Heavy Metal

Contamination

Microbial Contaminati

on from E. Coli

Microbial Contamination

from Staphylococcus

Microbial Contamination

from Pseudomonas

Microbial Contamintaion

from Salmonella

Capsule 0.043% 0.15% 0.28% 0.33% 0.31%

ACapsule

B0.064% 0.22% 0.31% 0.21% 0.29%

Capsule C

0.048% 0.24% 0.24% 0.23% 0.30%

Capsule D

0.053% 0.18% 0.34% 0.22% 0.27%

Total 0.051% 0.17% 0.27% 0.24% 0.28%

Question 20 ( answer to this is 69.7)

The probabilities of a positive response to two government programs from citizens in eight cities are given in the table. What is the chance of a positive response for program 1, given that the individual is from Houston?

City Positive Response to Program 1

Positive Response to Program 2

Atlanta 77.8% 82.1%Boston 86.4% 86.6%Chicago 65.9% 87.5%Dallas 73.8% 80.9%

Houston 69.7% 79.4%Los

Angeles78.4% 88.1%

Miami 82.5% 82.6%Newark 81.4% 83.3%

Total 68.8% 81.7%

Question 21

A pyramid has a square base with side s. The height of the pyramid is that of its side. What is the expression for the volume of the pyramid?

Question 22

What is the volume of the pyramids in these diagrams?

Question 23

Jack has a history project. He has to mold 20 slabs of clay into tiny pyramids. Each slab of clay contains 6 cubic inches of clay. Jack plans to make clay pyramids with a square base of 1 square inch and a height of 2 inches. What is the largest number of pyramids he can make from the 20 slabs of clay?

Question 24

The double cone is intersected by a vertical plane passing through the point where the tips of the cones meet. What is the shape of the cross section formed?

Question 25

Be able to understand cross sections of solids.

Question 26

In the diagram, the coordinates of endpoints A and B are (-6, 18) and (18, 10). What are the coordinates of point H?

Question 27

In the diagram, Line PR and Line AC are vertical lines, while Segment CB is a horizontal line segment. If CR : RB = 2 : 3, what are the coordinates of point Q?

Question 28

A coordinate plane has the floor plan for a rectangular swimming pool and the rectangular deck around it. The coordinates of the corners of the pool ABCD are at A(3,14) B ( 7,17) C(13,8) and D(9,6).

The corners of deck have coordinates at E( 0,14) F(9,20) G (17, 8) and H (9, 2).

What is th area of the deck around the pool ?

You should draw this to better understand :

Question 29

What is the ratio of the area of rectangle ABCF to the area of rectangle ABDE?

Question 30

Consider circle O. If BE = 12, EC = 6, and AE = 21, what is ED?

Question 31

Make sure you understand arcs and central angles.

Question 32

A ray of light is reflected off a mirror such that the reflected ray is perpendicular to the original ray, as shown in the diagram. Make sure you know what will happen in this case.

Question 33

Quadrilateral BCDE is inscribed in circle A. What is m E? ( answer is 103)

Question 34

Circle D circumscribes ABC and ABE. Which statements about the triangles are true?

Remember the following:

Statement I: The perpendicular bisectors of ABC intersect at the same point as those of ABE.Statement II: The distance from C to D is the same as the distance from D to E.

Question 35

A quadrilateral has vertices A(4, 5), B(2, 4), C(4, 3), and D(6, 4). Which statement about the quadrilateral is true?

ABCD is a parallelogram with noncongruent adjacent sides.

ABCD is a trapezoid with only one pair of parallel sides.

ABCD is a rectangle with noncongruent adjacent sides.

ABCD is a square.

ABCD is a rhombus with non-perpendicular adjacent sides.

Question 36

If the diameter of a circle has endpoints A(2,4) and B(9,4), where is the center of the circle? What is the standard form of the equation for this circle?

Question 37

If the diameter of a circle has endpoints A(14, 4) and B(-2, 16), where is the center of the circle? What is the standard form of the equation for this circle?

Question 38

What is the standard form of the equation of a circle that has its center at (-6, -9) and passes through the point (-6, 0)?

Question 39

If , what is the ratio of the length of to the length of ?

Question 40

The figure shows the layout of a symmetrical pool in a water park. What is the area of this pool rounded to the tens place? Use the value = 3.14. ( answer 2490 ft)