STAT 1350, Quiz #12, Summer 2014
Name _______________________________________
1-2. In many popular board games, a player rolls two dice and moves the number of spaces equal to the
sum shown on the dice. Here is the assignment of probabilities to the sum of the numbers on the up
faces when two fair dice are rolled:
1. Suppose Scott rolls a sum of 9 on his first roll. What is the probability that Jennifer will have
the same sum on her first roll?
A) 0
B) 4/6
C) 4/36
D) 9/36
E) 30/36
Ans: C
2. Suppose Scott and Jennifer each rolls a sum of 9 on their first rolls. What is the probability that
Quint will have a greater sum on his first roll?
A) 0
B) 1/6
C) 1/12
D) 5/18
E) 1
Ans: B
3. Back in the 17th century, some gamblers thought that the probability of at least one ace (i.e.,
one or more aces) when rolling two dice was 1/6 + 1/6. Is that true?
A)
Yes.
B)
No, it’s larger than 1/6 + 1/6.
C)
No, it’s smaller than 1/6 + 1/6.
D)
Sometimes it’s larger and sometimes it’s smaller.
E)
Impossible to say.
Ans: C
A household is a group of people living together at the same address. Choose one American household
at random and record how many people it contains. Here are the probabilities:
Number of people
Probability
1
?
2
0.32
3
0.17
4
0.16
5
0.07
6
0.02
7 or more
0.01
4. What is the probability that the household chosen contains only one person?
A)
0.15
D)
0.75
B)
0.25
E)
Can’t tell from the information given.
C)
0.35
Ans: B
5. What is the probability that a randomly chosen household contains four or more people?
A)
0.10
D)
0.90
B)
0.16
E)
Can’t tell from the information given.
C)
0.26
Ans: C
6. What is the probability that a randomly chosen household contains 8 people?
A)
0
D)
0.99
B)
0.01
E)
Can’t tell from the information given.
C)
0.001
Ans: E
7. A multiple-choice exam offers five choices for each question. Jason just guesses the answers,
so he has probability 1/5 of getting any one answer right. One of your math major friends tells
you that the assignment of probabilities to the number of questions Jason gets right out of 10
is (rounded to three decimal places):
Number right
Probability
0
.056
1
.188
2
.282
3
.250
4
.146
5
6
.058 .016
7
.003
8
.000
9
10
.000 .000
What is the probability that Jason will get no more than two of the ten questions right?
A) 0.244
B) 0.282
C) 0.526
D) 0.718
E) 0.756
Ans: C
Suppose we need to flip a coin, but we don’t have one. However, we do have a random number table
that we could use.
8. To simulate the outcome of tossing a coin you could assign random digits as follows:
A)
one digit simulates one toss; even digits are heads, and odd digits are tails.
B)
one digit simulates one toss; 0, 1, 2, 3, 4 are heads, and 5, 6, 7, 8, 9 are tails.
C)
one digit simulates one toss; 0, 1, 4, 6, 9 are heads, and 2, 3, 5, 7, 8 are tails.
D)
two digits simulate one toss; 00 to 49 are heads, and 50 to 99 are tails.
E)
Any of (A), (B), (C), (D) would work.
Ans: E
9. Suppose that 30% of students at your college would be willing to pay for the student
newspaper. Choose a student at random and ask whether he or she would pay. To simulate the
outcome, you could use one random digit with
A)
0, 1, 2, 3 meaning “Yes”
B)
1, 2, 3 meaning “Yes”
C)
0, 1, 2 meaning “Yes”
D)
Both (B) and (C) are correct.
E)
None of these is correct.
Ans: D
10. Light bulbs produced at the Lenin Electrical Works factory in Volgagrad are defective with
probability 0.12. To simulate the event that a single light bulb produced at the Lenin Electrical
Works is defective, the CIA could use two digits from a random generator with the convention
(choose the best answer)
A)
00, 01, 02, … , 09, 10, 11  defective
12, 13, 14, … , 97, 98, 99  nondefective
B)
01, 02, 03, … , 10, 11, 12  defective
13, 14, 15, … , 98, 99, 00  nondefective
C)
00, 01, 02, … , 85, 86, 87  nondefective
88, 89, 90, … , 97, 98, 99  defective
D)
Any of the above.
E)
None of the above.
Ans: D
11. Suppose you know the percentage of foul shots a basketball player makes during the season.
You want to estimate the expected number of shots made in 10 shots. You simulate 10 shots
25 times and get the following numbers of shots made:
7 9 7 6 3 7 5 6 5 6 7 5 6 6 8 5 6 3 9 6 7 7 8 7 9
Your estimate is:
A) 5.5
B) 6
Ans: C
C) 6.4
D) 6.7
E) 7
12. In government data, a family consists of two or more persons who live together and are
related by blood or marriage. Choose an American family at random and count the number of
people it contains. Here is the assignment of probabilities for your outcome:
Number of persons
Probability
2
0.42
3
0.23
4
0.21
5
0.09
6
0.03
7
0.02
Using the probabilities above, what is the expected size of the family you draw?
A) 2 people
B) 3 people
C) 3.14 people
D) 3.5 people
E) 4.5 people
Ans: C
13. Choose an adult woman at random. Here is the probability distribution for the number of
children the woman chosen has had:
Number of children
Probability
0
0.40
1
0.30
2
0.19
3
0.07
4
0.02
5
0.01
What is the expected value of the number of children a randomly chosen woman has had?
A) 1.00
B) 1.02
C) 1.42
D) 2.27
E) 2.5
Ans: B