Deck 19: Simulation

Question 1

Suppose you roll three fair six-sided dice. What is the probability of each die showing an even number (i.e., you roll no odd numbers)?

A) 1/3
B) 1/6
C) 1/8
D) 1/2
E) 0

Answer 1

1/8

Question 2

Bunches of bananas arriving from their supplier reach a grocer with probability 0.12 of being too ripe to sell. To simulate the event that a single bunch of bananas arriving at the grocery is too ripe to sell, the produce manager could use two digits from a random generator with the convention (choose the best answer):

A) 00, 01, 02, … , 09, 10, 11  too ripe
12, 13, 14, … , 97, 98, 99  acceptable
B) 01, 02, 03, … , 10, 11, 12  too ripe
13, 14, 15, … , 98, 99, 00  acceptable
C) 00, 01, 02, … , 85, 86, 87  too ripe
88, 89, 90, … , 97, 98, 99  defective
D) Any answer choice is correct.
E) None of the answer choices is correct.

Answer 2

Any answer choice is correct.

Question 3

Suppose flights at a large metropolitan airport are on-time 68% of the time and late 32% of the time. We want to use a table of random digits to simulate flight status (on-time or late), so we'll assign 01, 02, … , 68 to represent on-time flights, and 69, 70, … , 99, 00 to represent late flights.
You want to estimate the probability that 15 or more flights out of 20 will be on-time at this airport. You simulate 20 flights 25 times and get the following numbers of on-time flights:

What is your estimate of the probability?

A) 0.16
B) 0.48
C) 0.52
D) 0.56
E) 13

Answer 3

0.52

Question 4

China has 1.36 billion people. Soft drink manufacturers work constantly to try to carve out a portion of that huge market. A Euromonitor study in 2014 showed that Coca-Cola held 63% of the entire Chinese soft drink market. A researcher wants to simulate choosing 10 Chinese soft-drink consumers at random and asking each if he or she purchases Coca-Cola.
Use the correct assignment of digits from the previous question and the random digits below to simulate the answers of 10 Chinese citizens. Read across the row of random digits from left to right. How many of these 10 Chinese soft-drink consumers purchase Coca-Cola?

A) 4
B) 5
C) 6
D) 7
E) 8

Question 5

Computer voice recognition software is getting better. Some companies claim that their software correctly recognizes 98% of all words spoken by a trained user.
To simulate recognizing a single word when the probability of being correct is 0.98, you could use random digits as follows:

A) Two digits simulate one word; 00 to 97 mean "correct."
B) Two digits simulate one word; 00 to 98 mean "correct."
C) One digit simulates one word; 0 to 9 mean "correct."
D) Three digits simulate one word; 001 to 098 mean "correct."

Question 6

In a small Colombian village, 20 percent of the adults own a car, and 75 percent of the adults attend church regularly. Suppose that car ownership is independent of church attendance.
What is the probability that a randomly selected adult from this village owns a car and attends church regularly?

A) 0.95
B) 0.55
C) 0.20
D) 0.15
E) 0.05

Question 7

A researcher estimates that 30 percent of students at his college would be willing to pay for Google Fiber, the high-speed, superfast Internet access. The researcher chooses a student at random and asks that student if she would pay. To simulate the outcome, the researcher could use one random digit as follows:

A) Simulation 1: 0, 1, 2, 3 meaning "Yes"
B) Simulation 2: 1, 2, 3 meaning "Yes"
C) Simulation 3: 0, 1, 2 meaning "Yes"
D) Both simulations 2 and 3 are correct.
E) None of these answer choices is correct.

Question 8

Computer voice recognition software is getting better. Some companies claim that their software correctly recognizes 98% of all words spoken by a trained user.
The program recognizes words (or not) independently. To simulate the program's performance on 10 words, use two digits to simulate one word with 02 to 99 meaning "correct" and these random digits:

The number of words correct out of the 10 is

A)10.
B)9
C)8
D)2
E) 1.

Question 9

Suppose you toss a fair coin six times. What is the probability of all six tosses resulting in heads (i.e., you toss no tails)?

A) 1/64
B) 1/32
C) 1/6
D) 1/2
E) 0

Question 10

I want to use simulation to estimate the probability of getting exactly one head and one tail in two tosses of a fair coin. I assign the digits 0, 1, 2, 3, 4 to heads and 5, 6, 7, 8, 9 to tails. Using the following random digits to simulate, what is the estimate of the probability?

A) 1/10
B) 1/20
C) 0.6
D) 2/3
E) 0.5

Question 11

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.
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 the above would work.

Question 12

The WNBA player Temeka Johnson of the Los Angeles Sparks (2015) is a career 82 percent free-throw shooter. Suppose Tameka is fouled while attempting a three-point shot so she is awarded three free throws. What is the probability that she will make all three of her free throws?

A) 0.6724
B) 0.5514
C) 0.82
D) 0.18
E) 0

Question 13

In a small Colombian village, 20 percent of the adults own a car, and 75 percent of the adults attend church regularly. Suppose that car ownership is independent of church attendance.
What is the probability that a randomly selected adult from this village owns a car but does not attend church regularly?

A) 0.95
B) 0.55
C) 0.20
D) 0.15
E) 0.05

Question 14

Suppose you toss a fair coin and roll a fair six-sided die. What is the probability your actions result in tails on the coin and 3 on the die?

A) 1/8
B) 2/3
C) 1/6
D) 1/12
E) 0

Question 15

In a small Colombian village, 20 percent of the adults own a car, and 75 percent of the adults attend church regularly. Suppose that car ownership is independent of church attendance.
What is the probability that a randomly selected adult from this village does not own a car and does not attend church regularly?

A) 0.95
B) 0.55
C) 0.20
D) 0.15
E) 0.05

Question 16

A multiple choice exam offers four choices for each question. Jason just guesses the answers, so he has probability 1/4 of getting any one answer right. You want to simulate whether Jason's answers to 10 questions are right or wrong. One correct way to do this is

A) one digit from the random digit table simulates one answer, with 4 = right and all other digits = wrong. Ten digits from the table simulate 10 answers.
B) one digit from the random digit table simulates one answer, with 0 or 1 = right and all other digits = wrong. Ten digits from the table simulate 10 answers.
C) one digit from the random digit table simulates one answer, with odd = right and even = wrong. Ten digits from the table simulate 10 answers.
D) two digits from the random digit table simulate one answer, with 00 to 24 = right and 25 to 99 = wrong. Ten pairs of digits simulate 10 answers.
E) two digits from the random digit table simulate one answer, with 00 to 04 = right and 05 to 99 = wrong. Ten pairs of digits simulate 10 answers.

Question 17

Suppose flights at a large metropolitan airport are on-time 68% of the time and late 32% of the time. We want to use a table of random digits to simulate flight status (on-time or late), so we'll assign 01, 02, … , 68 to represent on-time flights, and 69, 70, … , 99, 00 to represent late flights.
Use the information above and these random digits to simulate 20 flights at this airport:

How many of the simulated flights were on-time?

A) 19
B) 15
C) 11
D) 10
E) 9

Question 18

Suppose you toss a fair coin twenty-six times and each time you observe heads (i.e., 26 heads in a row). What is the probability of heads on your next toss?

A) 1
B) 0.962
C) 0.5
D) 0.038
E) 0

Question 19

A book about bridge says that the probability that each of the four players is dealt exactly one ace is about 0.11. To simulate an outcome with probability 0.11, a person could do which of the following simulations:

A) Simulation 1: look at two digits in the random number table; the outcome occurs if the digits are 11.
B) Simulation 2: look at two digits in the random number table; the outcome occurs if the digits are any of 00, 01, ... , 11.
C) Simulation 3: look at two digits in the random number table; the outcome occurs if the digits are any of 00, 01, ... , 10.
D) Simulation 4: look at two digits in the random number table; the outcome occurs if the digits are any of 01, 02, ... , 11.
E) Both Simulations 3 and 4 are correct simulations.

Question 20

China has 1.36 billion people. Soft drink manufacturers work constantly to try to carve out a portion of that huge market. A Euromonitor study in 2014 showed that Coca-Cola held 63% of the entire Chinese soft drink market. A researcher wants to simulate choosing 10 Chinese soft-drink consumers at random and asking each if he or she purchases Coca-Cola.
One correct way to assign random digits to simulate the answer is

A) one digit simulates one person's answer; odd means "Yes" and even means "No."
B) one digit simulates one person's answer; 0 to 6 mean "Yes" and 7 to 9 mean "No."
C) two digits simulate one person's answer; 00 to 61 mean "Yes" and 62 to 99 mean "No."
D) two digits simulate one person's answer; 00 to 62 mean "Yes" and 63 to 99 mean "No."
E) There are 1.2 billion possible answers, which is too many to simulate.