Review Sheet 8, 11-19, 25
OBJ: Review for Probability Quest 2
1. Two cards are chosen at random from a deck of 52 cards without replacement. What is the
probability of getting two kings?
4/663
1/221
1/69
None of the above
4/52 · 3/51 = 12/2652 = 1/221
Two cards are chosen at random from a deck of 52 cards without replacement. What is the
probability that the first card is a jack and the second card is a ten?
3/676
1/169
4/663
None of the above
4/52 · 4/51 = 16/2652 = 4/663
On a math test, 5 out of 20 students got an A. If three students are chosen at random without
replacement, what is the probability that all three got an A on the test?
1/114
25/1368
3/400
None of the above
5/20 · 4/19 · 3/18 =60/6840 = 1/114
Three cards are chosen at random from a deck of 52 cards without replacement. What is the
probability of getting an ace, a king and a queen in order?
1/2197 8/5525 8/16575
None of the above
4/52 · 4/51 · 4/50 = 64/132600 = 8/16575
A school survey found that 7 out of 30 students walk to school. If four students are selected at
random without replacement, what is the probability that all four walk to school?
343/93960 1/783 7/6750
None of the above
7/30 · 6/29 · 5/28 · 4/27 =840/657720 = 1/783
13. One card is drawn from a regular
deck. What is the probability that it is a
queen if it is known to be a face card?
P(Q/F) = n(Q and F)/n(F) ( = P(Q and F)/P(F))
= 4
12
= 1
3
In New York State, 48% of all teenagers own a skate board, and 39% of all teenagers have
roller blades and a skate board. What is the probability that a teenager who has roller blades
also has a skate board?
87%
81%
123%
None of the above
P( SB/ RB) = P(SB  RB)/P(RB) = .39 ÷ .48 = .8125
At a middle school, 18% of all students play football and basketball, and 32% of all students
play football. What is the probability that a student who plays football also plays basketball?
56%
178%
50%
None of the above
P( BB/ FB) = P(BB F B)/P(FB) = .18 ÷ .32 = .5625
In the United States, 56% of all children get an allowance, and 41%of all children get an
allowance and do household chores. What is the probability that a child does household
chores given that he/she gets an allowance? 137%
97%
73%
None of the above
P( HC/ AL) = P(HC  AL)/P(AL) = .41 ÷ .56 = .7321
In Europe, 88% of all households have a television. 51% of all households have a television and
a VCR. What is the probability that a houshold with a television also has a VCR?
173%
58%
42%
None of the above
P(VCR/ TV) = P(VCR  TV/P(TV) = .51 ÷ .88 = .5795
In New England, 84% of the houses have a garage. 65% of the houses have a back yard and a
garage. What is the probability that a house has a backyard given that its has a garage?
77%
109%
19%
None of the above
P(G/ BY) = P(G  BY/P(BY) = .65 ÷ .84 = .7738
12) A pair of dice is thrown. Find the
probability that the dice match, given that
their sum is greater than five.
P(dice match/sum >5)
= 4
26
=2
13
(3,3)
(4,2) (4,3)
(5,1) (5,2) (5,3)
(6,1) (6,2) (6,3)
(2,4)
(3,4)
(4,4)
(5,4)
(6,4)
(1,5)
(2,5)
(3,5)
(4,5)
(5,5)
(6,5)
(1,6)
(2,6)
(3,6)
(4,6)
(5,6)
(6,6)
14. A pair of dice is thrown. Given that
their sum is > 9, find
a. P(sum is 8)
0
9
b. P(numbers match)
2= 1
10 5
c. P(sum is 12)
9
10
9
10
11
10
11
12
1
10
d. P(sum is even)
4= 2
10 5
e. P(sum is 9 or 10)
7
10
f. P(numbers match or sum is even)
2 + 4 _ 2
10
10
10
2/5
9
8)There are 4 navy socks and 6 black socks in your
drawer. One dark morning you randomly select 2 socks.
What is the probability that you will choose a navy pair?
• With Replacement • Without Replacement
4• 3
4 • 4_
10 9
10 10
2 • 1_
2 • 2_
5
3
5
5
2_
4_
15
25
25. There are 8 girls and 5 boys in my class. If I randomly
select 4 students to go to the board, find the following
(Use combination notation)
a. P(all girls) =
c. P(1 girl and 3
boys) =
8C4 •5C0
13C4
8C1 •5C3
b. P(2 girls and 2 boys) =
13C4
8C2 •5C2
13C4
The students that go to the board are to be 2 seniors and 2 juniors, who
are to be chosen at random from the 6 seniors and 7 juniors. If half of
the seniors and 4 juniors are girls find the probability that only girls go
up to the board(Use combination notation)
C
•
C
•
C
•
C
3 2 3 0 4 2 3 0
C
13 4
19a. (2c – 1)5
1( )5 – 5( )4 + 10( )3 – 10( )2 + 5( )1 – 1
1(2c)5 – 5(2c)4 + 10(2c)3 – 10(2c)2 + 5(2c)1– 1
32c5 – 5(16c4) + 10(8c3) – 10(4c2) + 5(2c) – 1
32c5 – 80c4 + 80c3 – 40c2 + 10c – 1
19b. third term of (3x +
1( )6 + 6( )5( )1 + 15( )4( )2
15(3x)4(2y)2
15(81x4)(4y2)
4860x4y2
6
2y)
16.While pitching for the Toronto Blue Jays, 4 out of every 7 pitches
that Juan Guzman threw in the first five innings were strikes. Find
the probability that three of his next four pitches will be strikes.
k(1-p)n-k
C
p
n k
n=4, k=3, p=4/7,1-p=3/7
3(3/7)1=
C
(4/7)
4 3
4 (43/73) (3/7)=
44•3 = 768
74 2401
From HW 6
6. What is the probability of
getting K #s in N rolls of a die?
P = 1/6
1-P = 5/6
9. A quiz has N multiple-choice
questions, each with # choices.
What is the probability of
getting K choices correct?
P = 1/#
1-P = 1- 1/#
17. Maria guessed at all 10 true/false
questions on her math test. Find:
a. P(7 correct) =
k
n-k
nCk p (1-p)
n=10, k=7, p=1/2, 1-p=1/2
7
3
10C7(1/2) (1/2) =
120 110 =
210
120 =
1024
15
128
b. P(all incorrect) =
k
n-k
nCk p (1-p)
n=10, k=0, p=1/2, 1-p=1/2
0
10
10C0(1/2) (1/2) =
1 110 =
210
1__
1024
c. P(at least 6 correct) =
k(1-p)n-k
C
p
n k
n=10, k > 6, p=1/2, 1-p=1/2
6(1/2)4 +
C
(1/2)
10 6
7(1/2)3 +
C
(1/2)
10 7
8(1/2)2 +
C
(1/2)
10 8
9(1/2)1 +
C
(1/2)
10 9
10(1/2)0
C
(1/2)
10 10
15)A dollar bill changer was tested with 100
one-dollar bills, of which 25 were counterfeit
and the rest were legal. The changer rejected
30 bills, and 6 of the rejected bills were
counterfeit. Construct a table, then find
a.
Incorporate the facts
given above into a
conditional chart.
R R
C
C
15)A dollar bill changer was tested with 100
one-dollar bills, of which 25 were counterfeit
and the rest were legal. The changer rejected
30 bills, and 6 of the rejected bills were
counterfeit. Construct a table, then find
a.
Incorporate the facts
given above into a
conditional chart.
R R
C
C
6
25
30
100
15)A dollar bill changer was tested with 100
one-dollar bills, of which 25 were counterfeit
and the rest were legal. The changer rejected
30 bills, and 6 of the rejected bills were
counterfeit. Construct a table, then find
R R
C
C
6
19 25
24 51 75
30 70 100
15)A dollar bill changer was tested with 100
one-dollar bills, of which 25 were counterfeit
and the rest were legal. The changer rejected
30 bills, and 6 of the rejected bills were
counterfeit. Construct a table, then find
R R
C
C
6
30
R R
25
100
C
C
6
19 25
24 51 75
30 70 100
15)A dollar bill changer was tested with 100
one-dollar bills, of which 25 were counterfeit
and the rest were legal. The changer rejected
30 bills, and 6 of the rejected bills were
counterfeit. Construct a table, then find
a.
b.
c.
The probability that a bill is legal
and it is accepted by the
machine.
P(CR)= 51
100
The probability that a bill is
rejected, given it is legal.
P(R/C)= 24 = 8
75 25
The probability that a
counterfeit bill is not rejected
P(R/C) = 19
25
R R
C
C
6
19 25
24 51 75
30 70 100
11)Of 200 students surveyed, 100 said
they studied for their math test. 105 said
they passed their test, and 80 said they
studied and passed their test.
a.
Incorporate the facts
given above into a
conditional chart.
P P
S
S
11)Of 200 students surveyed, 100 said
they studied for their math test. 105 said
they passed their test, and 80 said they
studied and passed their test.
a.
Incorporate the facts
given above into a
conditional chart.
P P
S
S
80
100
105
200
11)Of 200 students surveyed, 100 said
they studied for their math test. 105 said
they passed their test, and 80 said they
studied and passed their test.
P P
S
S
80
105
P P
100
200
S
S
80 20 100
25 75 100
105 95 200
11)Of 200 students surveyed, 100 said
they studied for their math test. 105 said
they passed their test, and 80 said they
studied and passed their test.
a) P(pass)
105
200
21
40
P P
S
S
80 20 100
25 75 100
105 95 200
11)Of 200 students surveyed, 100 said
they studied for their math test. 105 said
they passed their test, and 80 said they
studied and passed their test.
b) P(pass/studied) P(P/S)
80
100
4
5
P P
S
S
80 20 100
25 75 100
105 95 200
11)Of 200 students surveyed, 100 said
they studied for their math test. 105 said
they passed their test, and 80 said they
studied and passed their test.
_ _
c) P(P/S)
75
100
3
4
P P
S
S
80 20 100
25 75 100
105 95 200
18. The probability that a certain softball player gets
a hit is 1/5. (20%) In her next 5 at bats, find
b. P( at least 4 hits)
k(1-p)n-k
C
p
n k
n = 5, k ≥ 4, p = .2, 1–p=.8
c. P(at least 1 hit)
k(1-p)n-k
C
p
n k
n = 5, k ≥ 1, p = .2, 1–p=.8
4 (.8)1 + C (.2)5
C
(.2)
5 4
5 5
1 (.8)4+ C (.2)2 (.8)3
C
(.2)
5 1
5 2
3 (.8)2 + C (.2)4 (.8)1
C
(.2)
5 3
5 4
+ 5C5 (.2)5 OR
1 – 5C0 (.8)5
The problem on the quest,
n=10!!!
From HW 12 Conditional Worksheet 1. In a
study of the reading habits of 250 college
students it was found that 158 read Time
magazine, 139 read Newsweek, and 100 read
both Time and Newsweek
a.
Incorporate the facts
given above into a
conditional chart.
T T
N
N
From HW 12 Conditional Worksheet 1. In a
study of the reading habits of 250 college
students it was found that 158 read Time
magazine, 139 read Newsweek, and 100 read
both Time and Newsweek
Incorporate the facts
given above into a
conditional chart.
T T
N
N
100
139
158
250
From HW 12 Conditional Worksheet 1. In a
study of the reading habits of 250 college
students it was found that 158 read Time
magazine, 139 read Newsweek, and 100 read
both Time and Newsweek
T T
N
N
100
158
T T
139
250
N
N
100 39 139
58 53 111
158 92 250
From HW 12 Conditional Worksheet 1. In a study of
the reading habits of 250 college students it was
found that 158 read Time magazine, 139 read
Newsweek, and 100 read both Time and Newsweek.
Find the probability that a student:
a. Reads Newsweek P(N)
139
250
100 39 139
b. Reads both Time and
Newsweek P(T  N)
53 111
100
2
250
5
158 92 250
T T
N
N 58
From HW 12 Conditional Worksheet 1. In a study of
the reading habits of 250 college students it was
found that 158 read Time magazine, 139 read
Newsweek, and 100 read both Time and Newsweek.
Find the probability that a student:
c. Reads Newsweek given
reads Time P(NT)
100
50
100
39
139
158
79
d. Read Time given reads
53 111
Newsweek P(T/N)
100/139
158 92 250
T T
N
N 58
From HW 12 Conditional Worksheet 4.Out of 1000 students
surveyed, 10% reported that they had had a car accident
since getting their license, 40% reported driving more than
10,000 miles since getting their license and 6% had driven
more than 10,000 miles and had an accident.
a.
Incorporate the facts
given above into a
conditional chart.
A A
M
M
From HW 12 Conditional Worksheet 4.Out of 1000 students
surveyed, 10% reported that they had had a car accident
since getting their license, 40% reported driving more than
10,000 miles since getting their license and 6% had driven
more than 10,000 miles and had an accident.
Incorporate the facts
given above into a
conditional chart.
A A
M
M
60
400
100
1000
From HW 12 Conditional Worksheet 4.Out of 1000 students
surveyed, 10% reported that they had had a car accident
since getting their license, 40% reported driving more than
10,000 miles since getting their license and 6% had driven
more than 10,000 miles and had an accident.
Incorporate the facts
given above into a
conditional chart.
A A
M
M
60
340 400
40 560 600
100 900 1000
From HW 12 Conditional Worksheet 4.Out of 1000 students
surveyed, 10% reported that they had had a car accident
since getting their license, 40% reported driving more than
10,000 miles since getting their license and 6% had driven
more than 10,000 miles and had an accident
A A
60
M
A A
400
M
100
1000
M
M
60
340 400
40 560 600
100 900 1000
From HW 12 Conditional Worksheet 4.Out of 1000 students
surveyed, 10% reported that they had had a car accident since
getting their license, 40% reported driving more than 10,000 miles
since getting their license and 6% had driven more than 10,000
miles and had an accident. Find the probability that a student
a. Had driven more than
10000 miles without
having an accident.
P(M  A)
340
17
1000
50
b. Had driven no more
than 10000 miles and
did not have an __
accident. P(M  A)
560
1000
14
25
A A
M
M
60
340 400
40 560 600
100 900 1000
From HW 12 Conditional Worksheet 4.Out of 1000 students
surveyed, 10% reported that they had had a car accident since
getting their license, 40% reported driving more than 10,000 miles
since getting their license and 6% had driven more than 10,000
miles and had an accident. Find the probability that a student
c. Who drove no more
than 10,000 miles
had an accident.
P(M/A) 40
1
600 15
d. Who did not have an
accident drove more
than 10,000 miles.
P(A/M) 340/900=17/45
A A
M
M
60
340 400
40 560 600
100 900 1000