Question 1

Compute Probabilities of Binomial Experiments
-The probability that a football game will go into overtime is 13%. What is the probability that two of three football games will go to into overtime
A) 0.044
B) 0.13
C) 0.295
D) 0.0169

Accepted Answer

The probability of exactly two games going into overtime in a binomial experiment with n=3 trials and probability p=0.13 is calculated using the binomial probability formula: P(X=k) = C(n,k) * p^k * (1-p)^(n-k). Here, P(X=2) = C(3,2) * (0.13)^2 * (0.87)^1 = 3 * 0.0169 * 0.87 = 0.044.

Question 2

Compute Probabilities of Binomial Experiments
-According to insurance records a car with a certain protection system will be recovered 95% of the time. Find the probability that 5 of 8 stolen cars will be recovered.
A) 0.005
B) 0.625
C) 0.95
D) 0.05

Accepted Answer

The probability of recovering exactly 5 out of 8 cars can be calculated using the binomial probability formula: P(X=k) = C(n, k) * p^k * (1-p)^(n-k), where n=8, k=5, and p=0.95.

Question 3

Compute Probabilities of Binomial Experiments
-A quiz consists of 10 multiple choice questions, each with five possible answers, one of which is correct. To pass the quiz a student must get 60% or better on the quiz. If a student randomly guesses, what is the probability that the student will pass the quiz
A) 0.006
B) 0.060
C) 0.377
D) 0.205

Accepted Answer

To pass the quiz, a student must correctly answer 6 or more out of 10 questions. The probability of guessing any one question correctly is 1/5 (or 0.2), and incorrectly is 4/5 (or 0.8). This is a binomial experiment where n=10, p=0.2, and x≥6. The probability of passing by guessing (getting at least 6 out of 10 correct) is very low, and when calculated, it is closest to the option A) 0.006.

Question 4

Compute Probabilities of Binomial Experiments
-In a recent survey, 70% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 6 of them favor the building of the health center.
A) 0.023
B) 0.126
C) 0.429
D) 0.700

Accepted Answer

The probability of exactly 6 successes in 14 trials with a probability of success of 0.7 is given by the binomial distribution:P(X = 6) = (14 choose 6) * (0.7)^6 * (0.3)^8 = 0.126

Question 5

Compute Probabilities of Binomial Experiments
-According to government data, the probability that an adult was never in a museum is 15%. In a random survey of 10 adults, what is the probability that at least eight were in a museum
A) 0.820
B) 0.200
C) 0.002
D) 0.800

Accepted Answer

The probability that an adult was in a museum is 85% (100% - 15%). To find the probability that at least 8 out of 10 adults were in a museum, we calculate the probabilities for exactly 8, exactly 9, and exactly 10 adults being in a museum and sum these probabilities. Using the binomial probability formula, P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success, we calculate for k = 8, 9, and 10, and sum those probabilities. The sum gives us the probability of at least 8 adults being in a museum, which is approximately 0.820.

Question 6

Compute Probabilities of Binomial Experiments
-According to the Federal Communications Commission, 70% of all U.S. households have vcrs. In a random sample of 15 households, what is the probability that the number of households with vcrs is between 10 and 12, inclusive
A) 0.5947
B) 0.4053
C) 0.7
D) 0.2061

Accepted Answer

The probability of a household having a VCR is 0.7. To find the probability of having between 10 and 12 households (inclusive) with VCRs in a sample of 15, we use the binomial probability formula. Summing the probabilities for exactly 10, 11, and 12 households gives us the total probability, which matches choice A, 0.5947.

Question 7

Compute Probabilities of Binomial Experiments
-Fifty percent of the people that use the Internet order something online. Find the probability that only four of 8 Internet users will order something online.
A) 0.273
B) 0.500
C) 0.004
D) 4.375

Accepted Answer

The probability of exactly 4 out of 8 Internet users ordering something online in a binomial experiment can be calculated using the binomial probability formula: $P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$, where $n=8$, $k=4$, and $p=0.5$. Plugging these values in, we get $P(4) = \binom{8}{4}(0.5)^4(0.5)^4 = 70 \times 0.00390625 = 0.273$.

Question 8

Determine Whether a Probability Experiment is a Binomial Experiment
-If p is the probability of success of a binomial experiment, then the probability of failure is 
A) $1 - p$
B) -p
C) $\frac { x } { n }$
D) $\frac { \mathrm { n } } { \mathrm { x } }$

Accepted Answer

The probability of failure in a binomial experiment is 1 minus the probability of success, denoted as $1 - p$, where $p$ is the probability of success.

Question 9

Compute Probabilities of Binomial Experiments
-A recent survey found that 70% of all adults over 50 wear sunglasses for driving. In a random sample of 10 adults over 50, what is the probability that at least six wear sunglasses
A) 0.850
B) 0.700
C) 0.200
D) 0.006

Accepted Answer

This problem can be solved using the binomial distribution. Let X be the number of adults in the sample who wear sunglasses while driving. Then X follows a binomial distribution with parameters n = 10 and p = 0.7. The probability of at least 6 adults wearing sunglasses is the sum of the probabilities of 6, 7, 8, 9, and 10 adults wearing sunglasses. Using a binomial probability table or calculator, we get:

P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) 
= 0.2668 + 0.2335 + 0.1497 + 0.0574 + 0.0108 
= 0.7182

Therefore, the probability of at least six adults wearing sunglasses is 0.7182, which is closest to choice A) 0.850.

Question 10

Compute Probabilities of Binomial Experiments
-Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of at most three girls in ten births.
A) 0.172
B) 0.300
C) 0.003
D) 0.333

Accepted Answer

This is a binomial experiment with n = 10 (number of births) and p = 0.5 (probability of a girl birth). We want to find the probability of at most three girls, which means we want to find the probability of 0, 1, 2, or 3 girls. Using the binomial probability formula, we can find the probability of each of these scenarios and add them up:

P(X ≤ 3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)
= (10 choose 0) * (0.5)^0 * (0.5)^10 + (10 choose 1) * (0.5)^1 * (0.5)^9 + (10 choose 2) * (0.5)^2 * (0.5)^8 + (10 choose 3) * (0.5)^3 * (0.5)^7
= 0.0009765625 + 0.009765625 + 0.0439453125 + 0.1171875
= 0.172

Therefore, the best choice is A.

Question 11

Compute Probabilities of Binomial Experiments
-Sixty-five percent of men consider themselves knowledgeable soccer fans. If 14 men are randomly selected, find the probability that exactly four of them will consider themselves knowledgeable fans.
A) 0.005
B) 0.202
C) 0.65
D) 0.286

Accepted Answer

The probability of exactly four men considering themselves knowledgeable fans can be calculated using the binomial probability formula: P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where n = 14, k = 4, and p = 0.65. This calculation results in approximately 0.005.

Question 12

Compute Probabilities of Binomial Experiments
-Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of exactly nine girls in ten births.
A) 0.010
B) 0.9
C) 0.020
D) 0.09

Accepted Answer

The probability of exactly nine girls in ten births can be calculated using the binomial probability formula: $P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$, where $n=10$, $k=9$, and $p=0.5$ (since male and female births are equally likely). Plugging in these values, we get $P(X=9) = \binom{10}{9}(0.5)^9(0.5)^{10-9} = 10(0.5)^{10} = 0.010$.

Question 13

Compute Probabilities of Binomial Experiments
-According to the Federal Communications Commission, 70% of all U.S. households have vcrs. In a random sample of 15 households, what is the probability that at least 13 have vcrs
A) 0.1268
B) 0.7
C) 0.8732
D) 0.5

Accepted Answer

The probability of at least 13 households having VCRs out of 15 can be calculated using the binomial probability formula. Since the probability of success (having a VCR) is 0.7, we calculate the probability for exactly 13, 14, and 15 households having VCRs and sum these probabilities. The choice A) 0.1268 is the correct answer after performing these calculations.

Question 14

Compute Probabilities of Binomial Experiments
-According to government data, the probability that an adult was never in a museum is 15%. In a random survey of 10 adults, what is the probability that two or fewer were never in a museum
A) 0.820
B) 0.002
C) 0.800
D) 0.200

Accepted Answer

The probability of two or fewer adults never having been in a museum can be calculated using the binomial probability formula, which is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success. Here, n=10, p=0.15, and we need to calculate for k=0, 1, and 2, then sum those probabilities. The calculation yields a probability of approximately 0.820, making option A correct.

Question 15

Compute Probabilities of Binomial Experiments
-The probability that a house in an urban area will develop a leak is 5%. If 23 houses are randomly selected, what is the probability that none of the houses will develop a leak
A) 0.307
B) 0.050
C) 0.000
D) 0.002

Accepted Answer

The probability that a house will not develop a leak is 95% (100% - 5%). For 23 houses, the probability that none will develop a leak is (0.95)^23 ≈ 0.307.

Question 16

Compute Probabilities of Binomial Experiments
-A quiz consists of 10 true or false questions. To pass the quiz a student must answer at least eight questions correctly. If the student guesses on each question, what is the probability that the student will pass the quiz
A) 0.055
B) 0.8
C) 0.20
D) 0.08

Accepted Answer

The probability of passing the quiz (answering at least 8 out of 10 questions correctly) when guessing can be calculated using the binomial probability formula. The probability of success (correct answer) for each question is 0.5 (since the answer is either true or false with equal probability). To find the probability of getting at least 8 correct answers, we calculate the probability of getting exactly 8, exactly 9, and exactly 10 correct answers and sum these probabilities. The formula for the binomial probability of getting exactly k successes in n trials is P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where C(n, k) is the combination of n items taken k at a time, p is the probability of success on a single trial, and (1-p) is the probability of failure. Calculating this for 8, 9, and 10 successes and summing gives a probability of approximately 0.055, making option A correct.

Question 17

Determine Whether a Probability Experiment is a Binomial Experiment
-The trials of a binomial experiment must be mutually exclusive of each other.

Accepted Answer

The trials of a binomial experiment must be mutually exclusive of each other, meaning that the occurrence of one trial does not affect the probability of the occurrence of any other trial.

Question 18

Determine Whether a Probability Experiment is a Binomial Experiment
-Decide whether the experiment is a binomial experiment. If it is not, explain why. Selecting five cards, one at a time without replacement, from a standard deck of cards. The random variable is the number of picture cards obtained.

Accepted Answer

The answer of Determine Whether a Probability Experiment is a...

Question 19

Determine Whether a Probability Experiment is a Binomial Experiment
-Which of the below is not a requirement for binomial experiment
A) The trials are mutually exclusive.
B) The experiment is performed a fixed number of times.
C) For each trial there are two mutually exclusive outcomes.
D) The probability of success is fixed for each trial of the experiment.

Accepted Answer

The trials in a binomial experiment are not required to be mutually exclusive; instead, each trial must be independent, meaning the outcome of one trial does not affect the outcome of another.

Question 20

Compute Probabilities of Binomial Experiments
-The probability that an individual has 20-20 vision is 0.15. In a class of 32 students, what is the probability of finding five people with 20-20 vision
A) 0.190
B) 0.156
C) 0.000
D) 0.15

Accepted Answer

The probability of finding five people with 20-20 vision in a class of 32 students can be calculated using the binomial distribution. The probability of success (having 20-20 vision) is 0.15, and the number of trials (students) is 32. Using the binomial distribution formula, we can calculate the probability of finding exactly five people with 20-20 vision as:P(X = 5) = (32 choose 5) * (0.15)^5 * (0.85)^27 = 0.190Therefore, the probability of finding five people with 20-20 vision in a class of 32 students is 0.190, which is choice A.

Quiz 6: Discrete Probability Distributions

Compute Probabilities of Binomial Experiments -The probability that a football game will go into overtime is 13%. What is the probability that two of three football games will go to into overtime

Compute Probabilities of Binomial Experiments -According to insurance records a car with a certain protection system will be recovered 95% of the time. Find the probability that 5 of 8 stolen cars will be recovered.

Compute Probabilities of Binomial Experiments -In a recent survey, 70% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 6 of them favor the building of the health center.

Compute Probabilities of Binomial Experiments -According to government data, the probability that an adult was never in a museum is 15%. In a random survey of 10 adults, what is the probability that at least eight were in a museum

Compute Probabilities of Binomial Experiments -According to the Federal Communications Commission, 70% of all U.S. households have vcrs. In a random sample of 15 households, what is the probability that the number of households with vcrs is between 10 and 12, inclusive

Compute Probabilities of Binomial Experiments -Fifty percent of the people that use the Internet order something online. Find the probability that only four of 8 Internet users will order something online.

Determine Whether a Probability Experiment is a Binomial Experiment -If p is the probability of success of a binomial experiment, then the probability of failure is

Compute Probabilities of Binomial Experiments -A recent survey found that 70% of all adults over 50 wear sunglasses for driving. In a random sample of 10 adults over 50, what is the probability that at least six wear sunglasses

Compute Probabilities of Binomial Experiments -Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of at most three girls in ten births.

Compute Probabilities of Binomial Experiments -Sixty-five percent of men consider themselves knowledgeable soccer fans. If 14 men are randomly selected, find the probability that exactly four of them will consider themselves knowledgeable fans.

Compute Probabilities of Binomial Experiments -Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of exactly nine girls in ten births.

Compute Probabilities of Binomial Experiments -According to the Federal Communications Commission, 70% of all U.S. households have vcrs. In a random sample of 15 households, what is the probability that at least 13 have vcrs

Compute Probabilities of Binomial Experiments -According to government data, the probability that an adult was never in a museum is 15%. In a random survey of 10 adults, what is the probability that two or fewer were never in a museum

Compute Probabilities of Binomial Experiments -The probability that a house in an urban area will develop a leak is 5%. If 23 houses are randomly selected, what is the probability that none of the houses will develop a leak

Compute Probabilities of Binomial Experiments -A quiz consists of 10 true or false questions. To pass the quiz a student must answer at least eight questions correctly. If the student guesses on each question, what is the probability that the student will pass the quiz

Determine Whether a Probability Experiment is a Binomial Experiment -The trials of a binomial experiment must be mutually exclusive of each other.

Determine Whether a Probability Experiment is a Binomial Experiment -Which of the below is not a requirement for binomial experiment

Compute Probabilities of Binomial Experiments -The probability that an individual has 20-20 vision is 0.15. In a class of 32 students, what is the probability of finding five people with 20-20 vision