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Analytic Geometry EOC Quiz Answer Key
Statistics and Probability· (MCC9-12.S.ID.6a) Fit A Function To Data, (MCC9-12.S.CP.l) Events And Outcome Sets, (MCC912.S.CP.2) Independent Events, (MCC9-12.S.CP.3) Conditional Probability, (MCC9· 12.S.CP.4) Two-way Frequency Tables, (MCC9·
12.S.CP.S) Everyday Examples, (MCC9-12.S.CP.6) Find Conditional Probability, (MCC9·12.S.CP.7) Addition Rule
Date:------
Student N a m e : - - - - - - - - - - - - - - Teacher Name: Keith Simmons
Score:
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1)
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8
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2
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10
12
Number of Gallons of Gas
The graph displays the total cost when buying gas by the gallon. Which statement best describes the relationship between cost and
amount of gas purchased?
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The more gas you buy, the more it costs.
C)
The more gas you buy, the Less it costs.
B)
The Less gas you buy, the more it costs.
D)
It costs the same no matter how much gas you buy.
Explanation:
Since both the x and yvalues are increasing the relationship is positive. Therefore the correct statment is the more gas you buy, the
more it costs
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2)
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;,.:; coin 3 times. According to the tree diagram, how many possible outcomes exist?
i:·;;:'
A)
2
C)
6
G)
4
D)
8
Explanation:
The solution is 8. The 8 possibilities are as follows: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.
3)
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Chris and Hillary are remodeling their family room. They are deciding on the flooring, sofa and TV. How many possible combinations
are shown in the tree diagram?
A)
10
q
12
B)
11
D)
13
Explanation:
The solution is 12. The solution can be found by counting the choices or multiplying the choices for each category 3(2)(2)=12.
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4) Jane has 4 blue marbles, 3 red marbles, and 2 yellow marbles in a bag. Jane will randomly pick one marble from the bag. What is
the probability the marble will be yellow?
1
A)
7
1
9
B)
C)
D)
2
7
2
9
Explanation:
The probability that John will get a yellow marble is 2:9. There are 9 total marbles and 2 of them are yellow.
5) Michelle draws a card from a standard deck of 52 cards. She replaces the card and draws a second card. What is the probability
that she draws a red card and then a black card?
A)
1
16
C)
1
4
B)
1
26
D)
1
52
Explanation:
The solution is!_ Since the two events are independent, the outcome of one event does not affect the outcome of the other event.
4
26
To find the compound probability we multiply the probabilities of the two events. The probability of drawing a red card is
or.!:.
52
2
The same is true for the probability of drawing a black card.
1
1
2
1
4
. - =-
6) Michelle draws a card from a standard deck of 52 cards. She replaces the card and draws a second card. What is the probability
that she draws a Heart and then a Spade?
A)
1
16
C)
B)
1
26
D)
1
4
1
52
Explanation:
The solution is _.!_.Since the two events are independent, the outcome of one event does not affect the outcome of the other event
16
13
To find the compound probability we multiply the probabilities of the two events. The probability of drawing a Heart is
or I..
52
4
The same is true for the probability of drawing a Spade.
1
4
.!: = _.!:_
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7) Which event includes an example of a dependent event?
A)
A coin is flipped. The result is recorded. The
coin is then flipped a second time.
C)
A card is drawn from a standard deck of 52 cards. The card
is replaced and a second card is drawn.
B)
A die is rolled. The result is recorded. The die
is then rolled a second time.
D)
A bag contains red and green marbles. A marble is drawn
from the bag and is not replaced. A second marble is then
drawn from the bag.
Explanation:
The solution is B: A bag contains red and green marbles. A marble is drawn from the bag and is not replaced. Asecond marble is
then drawn from the bag. Since the first marble is not replaced, this impacts the probability of the second event. Thus it is a
dependent event.
8) Which situation describes INDEPENDENT events?
A die is rolled, then it is rolled a second time.
A)
One card is chosen from a standard deck, it is
B)
set aside, then a second card is drawn.
C)
D)
Tom chooses a Letter of the alphabet, then Beth must
choose a different Letter from the alphabet.
One student is chosen from Classroom A, then that student
chooses one of his friends from Classroom A
Explanation:
A die is rolled, then it is rolled a second time. The outcome of the first choice has no effect on the second choice.
9) In a lottery there are 9 balls, numbered 1 to 9, in each of three bins. One ball will be selected from each bin. What are the odds of
the numbers 2, 3, and 4 being pulled IN THAT ORDER7
A)
1to8
C)
1to503
B)
1 to 80
D)
1 to 728
~xplanation:
each event is independent. The chance of any number being pulled from the bin is
.!: The odds for all three balls are .!: x !:. x !:. =
9
9
9
9
- 1-, which means the odds are only 1 to 728 of this happening.
729
10) If a die is rolled twice, what is the probability of rolling a 5 and then a 2?
1
A)
C)
36
1
B)
D)
3
1
6
2
36
Explanation:
The solution is _..!__The two events are independent since the outcome of one event does not impact the outcome of the other
36
event To find the probability, multiply the probabilities together.
1
6
1
1
6
36
·- =-
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11) A bag contains blue and yellow marbles. Two marbles are drawn without replacement. The probability of selecting a blue marble
and then a yellow marble is 0.37, and the probability of selecting a blue marble on the first draw is 0.55.
;lhat is the probability of selecting a yellow marble on the second draw, if the first marble drawn was blue?
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B)
20%
D)
67%
Explanation:
To calculate probability of two dependent events you multiply their probabilities together. However, in this problem you were given
the probability of both dependent events occurring and solving for one of the dependent events. The solution is found by solving for
the second event:
P(blue and yellow)= P(blue)"P(yellow)
0.37 = 0.55 • P(yellow)
0 37
P(yellow)= · • 100% = 67%.
0.55
12) Mary Katherine has a bag of 3 red apples, 5 yellow apples and 4 green apples. Mary takes a red apple out of the bag and does
not replace it. What is the probability that the next apple she takes out is yellow?
A)
B)
5
44
4
11
C)
5
12
D)
5
11
Explanation:
The solution is 2_. Since Mary Katherine takes a red apple out of the bag, there are 11 apples left. Five of those apples are yellow.
11
So the probability of taking a yellow apple out of the bag is
2-.
11
13) In Salem, 82% of the households have cable television and Internet access and 90% of the houses have cable television. What is
the probability that a house has Internet access given that it has cable television?
A)
8%
C)
73%
~
~%
~
~
Explanation:
The solution is 91%. To solve this problem, we use the formula for conditional probability.
P(lnternetiCable) = P(Cable and Internet).
P(Cable)
14) At Bay High School60% of all students have a car and an Ipod and 70% of all students have a car. What is the probability that a
student with a car also has an lpod?
~
10%
q
~
B)
68%
D)
93%
Explanation:
The solution is 86%. To solve this problem, we use the formula for conditional probability.
P(lpodiCar) = P(Car and lpod).
P(Car)
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15)
Do you go to the movies at Least twice a week?
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LMale
~.- 35 i 45 .li
80 I
iFemale j 67 /28 1 9 5
I
1
__
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Jamie wants to find out how many students at her school go to the movies at least twice a week. She interviews 175 students and
records their gender and a yes if they go at least twice a week and no if they go Less than twice a week. She displays the results in
the table. What is the probability that a male goes to the movies at Least twice a week (round to the thousandth)?
A)
0.100
C)
0.343
B)
0.200
D)
0.438
Explanation:
The correct answer is 0.438. This is a conditional probability. Find the probability of someone going to the movies at least twice a
week given they are male. P(go to movies given that they are male}=
35
.
80
16) You are playing a game of Scrabble and have the SA tiles, 3 E tiles, 1 Z tile, 2M tiles, 3 L tiles, and 1 Y tile to choose from. What
is the probability that you choose E or Yon your next draw?
A)
B)
1
C)
s
1
3
D)
3
225
4
15
Explanation:
To find the probability we use the mutually exclusive probability formula P(A) + P(B). The probability of picking a E tile is.!: and the
s
probability of picking a Y tile is
I.. The sum is .i..
15
15
17) Timmy flipped a coin one hundred times. He got 62 heads and 38 tails. Which statement best describes this situation?
A)
B)
32% is the experimental probability of getting
a head on a coin flip in this situation.
62% is the theoretical probability of getting a
head on a coin flip.
q
62% is the experimental probability of getting a head on a
coin flip in this situation.
D)
68% is the theoretical probability of getting a tail on a coin
flip in this situation.
Explanation:
The correct statement is 62% is the experimental probability ofgetting a head on a coin flip in this situation.. Experimental is what
you get by doing the activity, theoretical probability if what you would expect to get, in this case 50·50.
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18) There are 10 marbles in a bag, and the marbles are either red or blue. Eric will randomly choose two marbles from the bag,
without replacing the first one. If the probability of both marbles' being red is
2_, how many BLUE marbles are in the
bag?
15
A)
3
C)
5
B)
4
D)
6
Explanation:
Eric's probability on the first pick is _2._ His probability of the second pick is x-l_ This will give a solution of x(x-l). }:_ is equal to
10
9
90 15
12
. 4 and 3 are the only consecutive numbers that when multiplied together equal 12. Therefore there are 4 red marbles in the bag
90
and 6 blue marbles.
19) There are 12 marbles in a bag, and the marbles are either yellow or green. Two marbles will be randomly picked from the bag,
without replacing the first one picked. The probability that both marbles will be yellow is
2.. How many GREEN marbles are in the
33
bag?
A)
4
C)
6
B)
5
D)
7
Explanation:
The probability of picking yellow first is -"-.The probability of picking yellow second is x- 1 . This will give a solution of x (x- 1), 2.
12
11
132 33
is equivalent to
~1ellow
lQ_, 5 and 4 are the only two consecutive numbers that when multiplied together equal 20. Therefore there are 5
132
and 7 green marbles in the bag.
20) You find a deck of cards and know that the deck has too many clubs and spades in it. The deck has 59 cards.
If you were to draw two cards without replacement, the probability of drawing a diamond and a club is
117
. How many extra
1711
spades are in the deck?
A)
2
C)
4
B)
3
D)
5
Explanation:
117
First set up a proportion of probability of diamond times-"- =
:
58 1711
117
13
. Solving for x tells you how many clubs are in the deck. Since x = 18 and there should only be 13 clubs then you
·-"- =
59 58 1711
have 5 extra clubs. With a total of 59 cards that means total you have 7 extra cards. If 5 of them are clubs then the other 2 must be
spades. So the deck has 2 extra spades.
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21) There are 15 cards, numbered 1 through 15. If you pick a card, what is the probability that you choose an odd number or a two?
A)
B)
2
C)
3
3
D)
5
8
15
8
225
Explanation:
There are 8 odd cards and one card is a two. Since 8 + 1 is 9, the probabitity is
~
15
or
~.
5
22) A cookie jar contains 6 chocolate chip cookies, 4 oatmeal cookies, 8 peanut butter cookies, and 2 sugar cookies. If a cookie is
pulled From the jar what is the probability that it is oatmeal or peanut butter?
A)
B)
1
C)
5
2
D)
5
3
5
4
5
Explanation:
These are mutually exclusive events so we use the formula P(A) + P(B).
The probability of picking an oatmeal cookie is..!. and the probability of picking a peanut butter cookie is"'}__ The sum of the
5
probabilities is
5
~.
5
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