Algebra II Regents Exam Questions by State Standard: Topic
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1
5
and P(B) =
, where A and B are
3
12
independent events, determine P(A ∩ B) .
PROBABILITY
563 Given P(A) =
S.CP.B.7: THEORETICAL PROBABILITY
560 The probability that Gary and Jane have a child
with blue eyes is 0.25, and the probability that they
have a child with blond hair is 0.5. The probability
that they have a child with both blue eyes and
blond hair is 0.125. Given this information, the
events blue eyes and blond hair are
I: dependent
II: independent
III: mutually exclusive
1 I, only
2 II, only
3 I and III
4 II and III
564 Given events A and B, such that P(A) = 0.6,
P(B) = 0.5, and P(A ∪ B) = 0.8 , determine whether
A and B are independent or dependent.
565 In contract negotiations between a local
government agency and its workers, it is estimated
that there is a 50% chance that an agreement will
be reached on the salaries of the workers. It is
estimated that there is a 70% chance that there will
be an agreement on the insurance benefits. There
is a 20% chance that no agreement will be reached
on either issue. Find the probability that an
agreement will be reached on both issues. Based
on this answer, determine whether the agreement
on salaries and the agreement on insurance are
independent events. Justify your answer.
561 A suburban high school has a population of 1376
students. The number of students who participate
in sports is 649. The number of students who
participate in music is 433. If the probability that a
student participates in either sports or music is
974
, what is the probability that a student
1376
participates in both sports and music?
S.CP.A.2: PROBABILITY OF COMPOUND
EVENTS
562 On a given school day, the probability that Nick
oversleeps is 48% and the probability he has a pop
quiz is 25%. Assuming these two events are
independent, what is the probability that Nick
oversleeps and has a pop quiz on the same day?
1 73%
2 36%
3 23%
4 12%
120
Algebra II Regents Exam Questions by State Standard: Topic
www.jmap.org
S.CP.A.3: CONDITIONAL PROBABILITY
S.CP.A.1: VENN DIAGRAMS
566 Data for the students enrolled in a local high school
are shown in the Venn diagram below.
568 Which situation best describes conditional
probability?
1 finding the probability of an event occurring
two or more times
2 finding the probability of an event occurring
only once
3 finding the probability of two independent
events occurring at the same time
4 finding the probability of an event occurring
given another event had already occurred
If a student from the high school is selected at
random, what is the probability that the student is a
sophomore given that the student is enrolled in
Algebra II?
85
1
210
85
2
295
85
3
405
85
4
1600
569 Sean's team has a baseball game tomorrow. He
pitches 50% of the games. There is a 40% chance
of rain during the game tomorrow. If the
probability that it rains given that Sean pitches is
40%, it can be concluded that these two events are
1 independent
2 dependent
3 mutually exclusive
4 complements
570 A fast-food restaurant analyzes data to better serve
its customers. After its analysis, it discovers that
the events D, that a customer uses the drive-thru,
and F, that a customer orders French fries, are
independent. The following data are given in a
report:
567 In a group of 40 people, 20 have brown hair, 22
have blue eyes, and 15 have both brown hair and
blue eyes. How many people have neither brown
hair nor blue eyes?
1 0
2 13
3 27
4 32
P(F) = 0.8
P(F ∩ D) = 0.456
Given this information, P(F | D) is
1 0.344
2 0.3648
3 0.57
4 0.8
121
Algebra II Regents Exam Questions by State Standard: Topic
www.jmap.org
571 Consider the probability statements regarding
events A and B below.
P(A or B) = 0.3;
P(A and B) = 0.2 ; and
P(A| B) = 0.8
What is P(B) ?
1 0.1
2 0.25
3 0.375
4 0.667
573 The probability that a resident of a housing
community opposes spending money for
community improvement on plumbing issues is 0.8.
The probability that a resident favors spending
money on improving walkways given that the
resident opposes spending money on plumbing
issues is 0.85. Determine the probability that a
randomly selected resident opposes spending
money on plumbing issues and favors spending
money on walkways.
572 Suppose events A and B are independent and
P(A and B) is 0.2. Which statement could be true?
1 P(A) = 0.4, P(B) = 0.3, P(A or B) = 0.5
2 P(A) = 0.8, P(B) = 0.25
3 P(A| B) = 0.2, P(B) = 0.2
4 P(A) = 0.15, P(B) = 0.05
574 A student is chosen at random from the student
body at a given high school. The probability that
the student selects Math as the favorite subject is
1
. The probability that the student chosen is a
4
116
junior is
. If the probability that the student
459
selected is a junior or that the student chooses Math
47
, what is the exact
as the favorite subject is
108
probability that the student selected is a junior
whose favorite subject is Math? Are the events
"the student is a junior" and "the student's favorite
subject is Math" independent of each other?
Explain your answer.
S.CP.A.4: CONDITIONAL PROBABILITY
575 Consider the data in the table below.
Male
Female
Right Handed
87
89
Left Handed
13
11
What is the probability that a randomly selected person is male given the person is left handed?
13
13
1
3
200
50
13
13
2
4
100
24
122
ID: A
560 ANS: 2
The events are independent because P(A and B) = P(A) ⋅ P(B) .
0.125 = 0.5 ⋅ 0.25
If P(A or B) = P(A) + P(B) − P(A and B) = 0.25 + 0.5 −.125 = 0.625, then the events are not mutually exclusive
because P(A or B) = P(A) + P(B)
0.625 ≠ 0.5 + 0.25
PTS: 2
561 ANS:
REF: 061714aii
P(S ∩ M) = P(S) + P(M) − P(S ∪ M) =
NAT: S.CP.B.7
TOP: Theoretical Probability
649
433
974
108
+
−
=
1376 1376 1376 1376
PTS: 2
562 ANS: 4
0.48 ⋅ 0.25 = 0.12
REF: 061629aii
NAT: S.CP.B.7
TOP: Theoretical Probability
PTS: 1
KEY: probability
563 ANS:
5
1 5
×
=
3 12 36
REF: 061811aii
NAT: S.CP.A.2
TOP: Probability of Compound Events
PTS: 2
REF: 012327aii
NAT: S.CP.A.2
TOP: Probability of Compound Events
KEY: probability
564 ANS:
P(A ∪ B) = P(A) + P(B) − P(A ∩ B) A and B are independent since P(A ∩ B) = P(A) ⋅ P(B)
0.8 = 0.6 + 0.5 − P(A ∩ B)
0.3 = 0.6 ⋅ 0.5
P(A ∩ B) = 0.3
PTS: 2
REF: 081632aii
KEY: independence
565 ANS:
0.3 = 0.3
NAT: S.CP.A.2
TOP: Probability of Compound Events
This scenario can be modeled with a Venn Diagram:
Since
P(S ∪ I) c = 0.2, P(S ∪ I) = 0.8. Then, P(S ∩ I) = P(S) + P(I) − P(S ∪ I) If S and I are independent, then the
= 0.5 + 0.7 − 0.8
= 0.4
Product Rule must be satisfied. However, (0.5)(0.7) ≠ 0.4. Therefore, salary and insurance have not been treated
independently.
PTS: 4
REF: spr1513aii
KEY: independence
NAT: S.CP.A.2
24
TOP: Probability of Compound Events
ID: A
566 ANS: 2
85
210 + 85
PTS: 2
567 ANS: 2
REF: 081818aii
NAT: S.CP.A.1
TOP: Venn Diagrams
40 − (20 + 22 − 15) = 13
PTS: 2
REF: 062204aii
NAT: S.CP.A.1
TOP: Venn Diagrams
568 ANS: 4
PTS: 2
REF: 012008aii
NAT: S.CP.A.3
TOP: Conditional Probability
569 ANS: 1
The probability of rain equals the probability of rain, given that Sean pitches.
PTS: 2
REF: 061611aii
570 ANS: 4
PTS: 2
TOP: Conditional Probability
571 ANS: 2
P(B) ⋅ P(A| B) = P(A and B)
NAT: S.CP.A.3
REF: 081824aii
TOP: Conditional Probability
NAT: S.CP.A.3
P(B) ⋅ 0.8 = 0.2
P(B) = 0.25
PTS: 2
REF: 081913aii
NAT: S.CP.A.3
TOP: Conditional Probability
572 ANS: 2
(1) 0.4 ⋅ 0.3 ≠ 0.2, (2) 0.8 ⋅ 0.25 = 0.2, (3) P(A| B) = P(A) = 0.2, (4) 0.2 ≠ 0.15 ⋅ 0.05
0.2 ≠ 0.2 ⋅ 0.2
PTS: 2
REF: 011912aii
NAT: S.CP.A.3
573 ANS:
P(A + B) = P(A) ⋅ P(B| A) = 0.8 ⋅ 0.85 = 0.68
TOP: Conditional Probability
PTS: 2
REF: 011928aii
NAT: S.CP.A.3
TOP: Conditional Probability
574 ANS:
1 116
31
1 116
47
≠ ⋅
= +
− P(M and J); No, because
459 4 459
108 4 459
P(M and J) =
PTS: 4
31
459
REF: 011834aii
NAT: S.CP.A.3
25
TOP: Conditional Probability
ID: A
575 ANS: 4
13
13
=
13 + 11 24
PTS: 2
576 ANS: 1
157
25 + 47 + 157
REF: 012011aii
NAT: S.CP.A.4
TOP: Conditional Probability
PTS: 2
577 ANS:
REF: 081607aii
NAT: S.CP.A.4
TOP: Conditional Probability
Based on these data, the two events do not appear to be independent. P(F) =
106
= 0.53, while
200
54
25
27
= 0.6 , P(F | R) =
= 0.39, and P(F | C) =
= 0.6. The probability of being female are not the
90
65
45
same as the conditional probabilities. This suggests that the events are not independent.
P(F | T) =
PTS: 2
REF: fall1508aii
578 ANS:
No, because P(M / R) ≠ P(M)
NAT: S.CP.A.4
TOP: Conditional Probability
NAT: S.CP.A.4
TOP: Conditional Probability
70
230
≠
180 490
0.38 ≠ 0.47
PTS: 2
579 ANS:
REF: 011731aii
A student is more likely to jog if both siblings jog. 1 jogs:
416
400
≈ 0.19. both jog:
≈ 0.22
2239
1780
PTS: 2
580 ANS:
103
103
=
110 + 103 213
REF: 061732aii
NAT: S.CP.A.4
TOP: Conditional Probability
PTS: 2
581 ANS:
REF: 061825aii
NAT: S.CP.A.4
TOP: Conditional Probability
P(F| L) =
PTS: 4
12
22
P(F) =
Since P(F| L) ≠ P(F) , the events are not independent.
27
45
REF: 061936aii
NAT: S.CP.A.4
26
TOP: Conditional Probability
ID: A
582 ANS:
No, because P(F / CR) ≠ P(F)
17 + 37 + 36 + 15
36
≠
42 + 36 39 + 17 + 42 + 12 + 17 + 37 + 36 + 15
36 105
≠
78 215
21
6
≠
13 43
PTS: 2
583 ANS:
Yes.
REF: 082231aii
NAT: S.CP.A.4
TOP: Conditional Probability
NAT: S.CP.A.4
TOP: Conditional Probability
P(Bl) = P(Bl| Gl)
0.14 + 0.26 =
.14
.35
.4 =.4
PTS: 2
584 ANS:
P(P / K) =
PTS: 4
585 ANS:
P(W / D) =
REF: 062229aii
P(P^K) 1.9
=
≈ 82.6% A key club member has an 82.6% probability of being enrolled in AP Physics.
P(K)
2.3
REF: 011735aii
TOP: Conditional Probability
NAT: S.CP.B.6
TOP: Conditional Probability
NAT: S.CP.B.6
TOP: Conditional Probability
P(W^D) .4
=
=.8
P(D)
.5
PTS: 2
REF: 081726aii
586 ANS:
165 + 66 − 33 198
=
825
825
PTS: 2
NAT: S.CP.B.6
REF: 081925aii
27