Deck 4: Probability and Probability Distributions

Question 1

What is the probability when a personal assessment is made without referencing data?

A) empirical probability
B) classical probability
C) subjective probability
D) exclusive probability

Answer 1

subjective probability

Question 2

The union of two events is denoted as

A) A $\subset$ S.
B) A $\cup$ B.
C) P(A $\cup$ B).
D) A $\cap$ B.

Answer 2

A $\cup$ B.

Question 3

Which rule is being followed when summing P(A) and P(B) then subtracting P(A $\cap$ B) from the sum?

A) complement
B) multiplication
C) addition
D) joint probability

Answer 3

addition

Question 4

Mutually exclusive events __________.

A) have joint probability of zero
B) contain the multiple of two probabilities
C) are conditional on interest
D) contain all possible experiment outcomes

Question 5

Using conditional probability, if P(A) = 0.60, P(B) = 0.25, and P(A $\cap$ B) = 0.05, then P(A | B) =

A) 0.40.
B) 0.08.
C) 0.20.
D) 5.00.

Question 6

Using conditional probability, if P(A) = 0.50, P(B) = 0.20, and P(A $\cap$ B) = 0.15, then P(A | B) =

A) 0.40.
B) 0.30.
C) 0.75.
D) 2.5.

Question 7

In Holland, 72% of the people own a car. If five adults are randomly selected, what is the probability that none of the four have a car?

A) 4.93%
B) 0.61%
C) 23.60%
D) 0.62%

Question 8

In Holland, 60% of the people own a car. If five adults are randomly selected, what is the probability that none of the five have a car?

A) 7.8%
B) 1.02%
C) 40%
D) 1.03%

Question 9

In Holland, 30% of the people own a car. If five adults are randomly selected, what is the probability that no more than two own a car?

A) 37.2% probability that more than two own a car.
B) 30.9% probability that more than two own a car.
C) 66.8% probability that no more than two own a car.
D) 83.7% probability that no more than two own a car.

Question 10

A simple event _____.

A) contains unlimited outcomes
B) contains exactly two outcomes
C) contains only subsets of the outcome
D) contains a single outcome

Question 11

Michael has interviewed for two jobs. He feels that he has a 56% chance of getting an offer on Job A and a 60% chance of getting an offer on Job B. He also believes there is a 60% chance of getting an offer on both jobs. What is the probability that he receives an offer on at least one of the jobs?

A) 0.60
B) 0.25
C) 0.10
D) 0.56

Question 12

Michael has interviewed for two jobs. He feels that he has a 65% chance of getting an offer on Job A and a 45% chance of getting an offer on Job B. He also believes there is a 40% chance of getting an offer on both jobs. What is the probability that he receives an offer on at least one of the jobs?

A) 0.60
B) 0.25
C) 0.10
D) 0.70

Question 13

Michael has interviewed for two jobs. He feels that he has a 65% chance of getting an offer on job A and a 45% chance of getting an offer on job B. He also believes there is a 40% chance of getting an offer on both jobs. What is the probability that he does not get an offer at either job?

A) 0.10
B) 0.30
C) 0.70
D) 0.25

Question 14

Two events are _____ if the occurrence of one event does not affect the probability occurrence of another.

A) simple
B) dependent
C) independent
D) comparative

Question 15

Which is not a characteristic of the normal distribution?

A) It is bell-shaped.
B) It is inverse.
C) It is asymptotic.
D) It is symmetric.

Question 16

Simone, owner of the Blue Canoe Coffee Shop, ran a report showing the identified valued customer visits the shop on average 12 times in a 60-day period. Simone now wants to break down the information further to determine how many visits she should expect in a 5-day period from a tracked value customer. How many visits should Simone expect?

A) 1
B) 3
C) 2
D) 4

Question 17

Simone, owner of the Blue Canoe Coffee Shop, ran a report showing the identified valued customer visits the shop on average 18 times in a 30-day period. Simone now wants to break down the information further to determine how many visits she should expect in a 5-day period from a tracked value customer. How many visits should Simone expect?

A) 3
B) 5
C) 1
D) 4

Question 18

A special case where the mean is equal to zero and the variance is equal to one is called _____.

A) normal distribution
B) standard normal distribution
C) corresponding value
D) standard normal variable

Question 19

Alex has been studying for the certified management exam. Results from the last exam indicate that the mean was 62 with a standard deviation of 5. He needs to be in the top 20% (80^th percentile) to pass. Use zvalue with two decimal places, 1.28, in your calculations. What score will place Alex in the top 20% of the distribution?

A) 68.40
B) 79.68
C) 83.12
D) 74.00

Question 20

Alex has been studying for the certified management exam. Results from the last exam indicate that the mean was 72 with a standard deviation of 6. He needs to be in the top 20% (80^th percentile) to pass. The z table indicates 1.28. What score will place Alex in the top 20% of the distribution?

A) 79.68
B) 83.12
C) 74
D) 79.28

Question 21

The Daytona 500 runs 40 race cars. Of the 40, 19 cars crashed. This is a probability of 0.475 that a car will crash in the race. This is an example of which probability?

A) subjective
B) empirical
C) classical
D) random

Question 22

Which is the best probability to determine the outcome of rolling seven with two dice?

A) subjective
B) empirical
C) classical
D) random

Question 23

Which one does not satisfy the Poisson process?

A) Success is presented as an integer between one and infinity.
B) Number of successes counted in nonoverlapping intervals are independent.
C) The interval is the same for probability failure as in success in exceeding the size of the interval.
D) Probability of success in an interval is the same for all intervals of equal size and proportionality.

Question 24

Events are considered _____ if they include all outcomes in the sample space.

A) posterior
B) exhaustive
C) a sample
D) a rule

Question 25

The intersection of two events is denoted as __________.

A) A $\cap$ B
B) A $\cup$ B
C) P (A $\cup$ B) ²
D) P (A^c) = 1 - P(A)

Question 26

Marketing analysis determined 49% of females between the ages of 25 and 34 years search for green technology and practice being green, as compared to 37% of men in the same age group. What is the probability that a randomly selected woman between the age of 25 and 34 does not search for green technology?

A) 68% probability
B) 56% probability
C) 51% probability
D) 44% probability

Question 27

Marketing analysis determined 44% of females between the ages of 25 and 34 years search for green technology and practice being green, as compared to 32% of men in the same age group. What is the probability that a randomly selected woman between the age of 25 and 34 does not search for green technology?

A) 12% probability
B) 68% probability
C) 56% probability
D) 44% probability

Question 28

Marketing analysis determined 55% of females between the ages of 25 to 34 years old search for green technology and practice being green, as compared to 33% of men in the same age group. What is the probability that a randomly selected man between the age of 25 and 34 does not search for green technology?

A) 44% probability
B) 67% probability
C) 12% probability
D) 68% probability

Question 29

Marketing analysis determined 44% of females between the ages of 25 to 34 years old search for green technology and practice being green, as compared to 32% of men in the same age group. What is the probability that a randomly selected man between the age of 25 and 34 does not search for green technology?

A) 44% probability
B) 68% probability
C) 32% probability
D) 56% probability

Question 30

The _____ of the discrete random variable X, denoted by E(X), or simply $\mu$ , is a weighted average of all possible values of X.

A) summary value
B) corresponding value
C) random value
D) expected value

Question 31

Howard Simpson at Organics Central Market ran a report showing the identified valued customer visits the market on average 12 times in a 30-day period. Howard now wants to break down the information further to determine how many visits he should expect in a 5-day period from a tracked value customer. What is the probability of a valued customer visiting all 5 days?

A) 4%
B) 10%
C) 8%
D) 9%

Question 32

Howard Simpson at Organics Central Market ran a report showing the identified valued customer visits the market on average 18 times in a 30-day period. Howard now wants to break down the information further to determine how many visits he should expect in a 5-day period from a tracked value customer. What is the probability of a valued customer visiting all 5 days?

A) 10%
B) 8%
C) 4%
D) 9%

Question 33

Which theorem can the posterior probability be found using the prior probability and conditional probability?

A) Fisher
B) Poisson
C) Bernoulli
D) Bayes'

Question 34

Andrea decided her job opportunities will increase conditional on completing her bachelor's degree. Based on her assumption, what probability would best fit?

A) classical probability
B) conditional probability
C) complement rule
D) empirical probability

Question 35

Based on the provided table, the expected employee bonus is 3.05 or 3,050. What is the variance and the standard deviation of the annual bonus amount?

A) $\sigma$ =9.36=3.059
B) $\sigma$ =4.95=2.225
C) $\sigma$ =9.85=3.138
D) $\sigma$ =11.47=3.387

Question 36

Based on the provided table, the expected employee bonus is 4.95 or 4,950. What is the variance and the standard deviation of the annual bonus amount?

A)
B)
C)
D)

Question 37

Tiffany Ham's business is thriving in Houston, TX. To reward her team, Tiffany is implementing a performance incentive program. Annual Bonuses begin at $5,000 for excellent performance, $3,000 for good performance, and $1,500 for fair performance, and $0 for poor performance.

- The probability levels are 0.10, 0.45, 0.35, and 0.15, respectively. What is the expected value of the annual bonus amount for an employee?

A) $1,875
B) $2,300
C) $2,375
D) $2,325

Question 38

Tiffany Ham's business is thriving in Houston, TX. To reward her team, Tiffany is implementing a performance incentive program. Annual Bonuses begin at $5,000 for excellent performance, $3,000 for good performance, and $1,500 for fair performance, and $0 for poor performance.

-The probability levels are 0.15, 0.40, 0.25, and 0.20, respectively. What is the expected value of the annual bonus amount for an employee?

A) $1,875
B) $2,300
C) $2,325
D) $2,375

Question 39

In reviewing retirement portfolios, Kim determined the probability of a client owning stock is 0.50 and the probability of owning a bond is 0.20. The probability of a customer who owns bonds already owning stock is 0.55. What is the probability a client owns both securities in their retirement portfolio?

A) 0.30
B) 0.40
C) 0.39
D) 0.28

Question 40

In reviewing retirement portfolios, Kim determined the probability of a client owning stock is 0.70 and the probability of owning a bond is 0.40. The probability of a customer who owns bonds already owning stock is 0.55. What is the probability a client owns both securities in their retirement portfolio?

A) 0.52
B) 0.30
C) 0.40
D) 0.39

Question 41

Alison has been hired to sell two different homes on the same street that two houses apart. She predicts that Home A has a 57% chance in selling on the first week of being listed, whereas Home B is in lesser condition and has a 34% probability. There is also a 14% chance both homes will not sell on the first week of it being listed. What is the probability that house A does not sell given that house B does not sell due to it's poor condition?

A) 0.267
B) 0.212
C) 0.667
D) 0.250

Question 42

Alison has been hired to sell two different homes on the same street that two houses apart. She predicts that Home A has a 75% chance in selling on the first week of being listed, whereas Home B is in lesser condition and has a 30% probability. There is also a 20% chance both homes will not sell on the first week of it being listed. What is the probability that house A does not sell given that house B does not sell due to it's poor condition?

A) 0.267
B) 0.286
C) 0.250
D) 0.700

Question 43

The sample space contains all probable outcomes of an experiment.

Question 44

If 42% of interns are between the ages of 20 to 25, the complement rule dictates P(A^c) = 1 - P(A) = 1 - 0.42 = 0.58.

Question 45

According to the total probability rule, P(A) equals the sum of P(A $\cap$ B) and P(A $\cap$ B^c), and is considered conditional on two mutually exclusive and exhaustive events independent of an experiment.

Question 46

Bayes' theorem is a procedure for updating probabilities based on new information.

Question 47

A discrete random variable is denoted as distinct countable values x₁, x₂, x₃,…

Question 48

A result of attaching probabilities to the outcomes of a Bernoulli process is called a binomial distribution.

Question 49

The Poisson process is satisfied only if the number of successes counted in nonoverlapping intervals is independent and is not dependent on the proportional size of an interval.

Question 50

The Gaussian distribution is the most extensively used probability distribution in statistical work.