SB 4.1-4.5
What is the difference between (a) the addition rule and (b) the addition rule for two mutually exclusive events?
(a) requires you to subtract the probability of intersection, (b) does not.
Which of the following symbols denotes the complement of an event A?
(bar over) A
A bottle of liquid laundry detergent has a 0.02 probability of being improperly filled. There is a 0.03 probability that the label on the bottle will not be affixed properly. If the events of bottle fill and affixing the label are independent, what is the probability of a bottle being filled improperly and having an improperly affixed label?
0.0006
The probability of an employee getting a promotion is 0.20. The probability of an employee having an MBA is 0.30. The probability of an employee getting a promotion, given that the employee has an MBA, is 0.25. What is the probability that an employee has an MBA and gets a promotion?
0.075
Corky and Lori process purchase orders for Acme Inc. Lori processes 60% of the purchase orders. Corky processes the remaining 40% of the purchase orders. While 5% of Lori's purchase orders have errors, only 2.5% of Corky's purchase orders have errors. A purchase order has an error. What is the probability that Lori processed the erroneous purchase order?
0.75
The probability that a customer orders popcorn is 0.40. The probability that a customer orders a drink is 0.65. The probability that a customer orders popcorn and a drink is 0.30. If a customer has already ordered popcorn, what is the probability that the customer will order a drink?
0.75
Consider an event A and its complement (bar over)A. What is P(A) + P((bar over)A)?
1
The probability assigned to an experimental outcome must be between zero and ______
1
The conditional probability of A, given B, is calculated by dividing the probability of the intersection of A and B by the probability of ______
B
When new information is used to revise a prior probability to a posterior probability, which of the following methodologies is used?
Bayes' Theorem
Which rule is defined as P(A | B) = P(A∩B)/(P(B))?
Conditional Probability Rule
Which of the following notations stands for "the probability of A, given B"?
P(A | B)
events A and B are mutually exclusive, then ______.
P(A ∩ B) = 0
Given any two events, A and B, the multiplication rule states that ______
P(A ∩ B) = P(A) × P(B | A)
Let A and B be independent events. The probability that A and B will both occur is ______
P(A ∩ B) = P(A) × P(B)
Let A and B be mutually exclusive events. The simplest way of writing the probability that A or B will occur is ______
P(A ∪ B) = P(A) + P(B)
Consider an event A. What is the probability that A will not occur?
P(A) = 1 - P(A)
The conditional probability of A, given B, is calculated by: P(A | B) =
P(A∩B)/(P(B))
The conditional probability of A, given B, is calculated by: P(A | B) =
P(A∩B)/(P(B))
The formula P(A ∩ B) = P(A) × P(B | A), is known as
The Multiplication Rule for any two events
Consider an event A. The representation: P((tilt bar over)A) is interpreted as:
The complement of event A
If an experiment consists of a three step process, what do the number of branches shown at stage three tell us?
The number of outcomes in the sample space
The intersection of Events A and B is represented as P(A∩B). This is interpreted as:
The probability of both A and B occurring together
The union of Events A and B is represented as P(A∪B). This is interpreted as
The probability of both A or B, or both occurring
Which of the following is an example of a conditional probability?
The probability that a student plays video games given that the student is female.
True or false: If the events A1, A2, ..., AN are independent, then P(A1 ∩ A2 ∩ ... ∩ AN) = P(A1) × P(A2) × ... × P(AN)
True
When can the classical method of computing probabilities be used?
When all of the sample space outcomes are equally likely.
The ______ of an event is the opposite of an event. It is the set of all outcomes of an experiment that are not included in an event
complement
The probability of event A, given that event B has occurred, is known as the ______ probability of A, given B.
conditional
True or false: The probability of an experimental outcome can be less than 0
false
If we claim that the probability of rolling a three with a fair die is 1/6, then we mean that
in many rolls of a fair die, we will roll a 3 about one sixth of the time
If we claim that the probability of rolling a three with a fair die is 1616, then we mean that
in many rolls of a fair die, we will roll a 3 about one sixth of the time
If the events A1, A2, ..., AN are _______, then P(A1 ∩ A2 ∩ ... ∩ AN) = P(A1) × P(A2) × ... × P(AN)
independent
The multiplication rule is used to calculate ______
the probability of the intersection of two events.
The addition rule is used to calculate ______
the probability of the union of two events.
The probability of a student not skipping class is 0.90. What is the probability that a student does skip class?
0.10
The probability of a household having at least one pet is 0.80. What is the probability that a household does not have any pets?
0.20
Corky and Lori process purchase orders for Acme Inc. Lori processes 60% of the purchase orders. Corky processes the remaining 40% of the purchase orders. While 5% of Lori's purchase orders have errors, only 2.5% of Corky's purchase orders have errors. A purchase order has an error. What is the probability that Corky processed the erroneous purchase order?
0.25
What is the probability of selecting a diamond from a standard deck of cards?
0.25
A bag is full of marbles. You reach in and pull out a single marble. If P(red) = 0.10, P(blue) = 0.05, P(green) = 0.25, P(yellow) = 0.30, and P(purple) = 0.30, then what is the probability of selecting a blue or yellow marble?
0.35
A bag is full of marbles. You reach in and pull out a single marble. If P(red) = 0.10, P(blue) = 0.05, P(green) = 0.25, P(yellow) = 0.30, and P(purple) = 0.30, then what is the probability of selecting a red or yellow marble?
0.40
The probability of Margaret receiving a promotion is 0.70. The probability of Katia receiving a promotion is 0.60. If the two promotions are independent, what is the probability of both Margaret and Katia receiving a promotion?
0.42
What is the probability of rolling an even number on a six-sided die?
0.50
An experiment is performed many times. The probabilities of the experimental outcomes are estimated to be the proportion of the time that the outcomes occurred during the many repetitions of the experiment. These are called ______ probabilities
relative frequency
In a particular industry, it is known that 82% of companies ship their products by truck and 47% of companies ship their products by rail. 40% of companies ship their products by truck and rail. The probability that a company ships by truck or rail or both is ______.
0.89
An event that is guaranteed to occur has probability equal to _____
1, one, or 100%
The probability of Event B occurring is represented by P(B). Which of the following represents the probability of Event B not occurring?
1- P(B)
Let A and B be events. The probability that A or B (or both) will occur is ______
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Which method of computing probabilities states that: The probability of an event occurring = Number of sample space outcomes that correspond to the event / (Total number of sample space outcomes)
the classical method
If two events are independent, then the probability that both events occur equals ______
the product of the individual probabilities.
True or false: If the events A1, A2, ..., AN are mutually exclusive, then P(A1 ∪ A2 ∪ ... ∪ AN) = P(A1) + P(A2) + ... + P(AN)
true
The probability that a customer orders popcorn is 0.40. The probability that a customer orders a drink is 0.65. The probability that a customer orders popcorn and a drink is 0.30. If a customer has already ordered a drink, what is the probability that the customer will order popcorn?
0.46
The probability that Anthony is on time for work is 0.90. The probability that Anthony takes the train to work is 0.80. Given that Anthony takes the train to work, the probability that he is on time is 0.95. What is the probability that Anthony is on time for work and takes the train?
0.76
Kareem is trying to decide which college to attend full time next year. Kareem believes there is a 55% chance that he will attend State College and a 33% chance that he will attend Northern University. The probability that Kareem will attend either State or Northern is ______
0.88
If a sample space can be divided into S1 and S2, two mutually exclusive states of nature, and we know P(S1), P(S2), P(E | S1), and P(E | S2), how do we find P(S1 | E)?
P(S1 | E) = P(S1)×P(E|S1) / (P(S1)×P(E|S1)+P(S2)×P(E|S2))
Consider an event A. The representation: P((bar over)A) is interpreted as
The probability of event A not occurring
If the probability of an event is not influenced by another event occurring, then the two events are ______
dependent
The probability of Murali going to the coffee shop is 0.70. The probability of Connie going to the coffee shop is 0.40. If Murali goes to the coffee shop, the probability of Connie going to the coffee shop is 0.48. The events Murali goes to the coffee shop and Connie goes to the coffee shop are ______
dependent
Events A and B are ______ events if they have no sample space outcomes in common.
mutually exclusive
If the events A1, A2, ..., AN are _________, then P(A1 ∪ A2 ∪ ... ∪ AN) = P(A1) + P(A2) + ... + P(AN)
mutually exclusive
If two events cannot occur at the same time, they are said to be:
mutually exclusive
The _____ of an event is the likelihood that the event will occur.
probability
The ______ of an event is the sum of the probabilities of the sample space outcomes that correspond to the event
probability
An experiment was conducted where people were asked to choose a number between 1 and 10. Out of the 204 people asked, 61 chose the number 7. If we claim the probability of picking the number 7 is 61/204 = 0.30, we are using a ______ probability.
relative frequency
The ______ of an experiment is the set of all possible experimental outcomes
sample space
A softball coach believes that Laurie has a 0.5 probability of getting a hit against a particular pitcher that Laurie has never batted against before. This is called a(n) ______ probability
subjective
A stock broker believes that a certain market price will double next year with a probability of 0.65. This is called a(n) ______ probability.
subjective
Suppose an experiment consists of tossing a coin two times. Which of the following would represent the sample space for this experiment?
{HH, HT, TH, TT}
Suppose an experiment consists of shooting basketball free throw two times. Which of the following would represent the sample space for this experiment? S = Shot made it in the basket M = Shot missed the basket
{SS, SM, MS, MM}