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Questions and Answers
According to Statistics Canada's 2016 data on degree grants, if an employer randomly selects a graduate, what is the probability that the person chosen is female?
According to Statistics Canada's 2016 data on degree grants, if an employer randomly selects a graduate, what is the probability that the person chosen is female?
- Approximately 0.43
- Approximately 0.57 (correct)
- Approximately 0.70
- Approximately 0.30
If an employer randomly picks a graduate without considering the degree level, what is the probability that the selected person holds a doctoral degree, based on the Statistics Canada 2016 data?
If an employer randomly picks a graduate without considering the degree level, what is the probability that the selected person holds a doctoral degree, based on the Statistics Canada 2016 data?
- Approximately 0.057
- Approximately 0.124
- Approximately 0.025 (correct)
- Approximately 0.209
According to the odds presented, which event has a higher probability of occurring than being killed in a traffic accident while driving 16 kms to buy a lottery ticket?
According to the odds presented, which event has a higher probability of occurring than being killed in a traffic accident while driving 16 kms to buy a lottery ticket?
- Finding a four-leaf clover (correct)
- Winning the lottery
- Dying in a storm
- Being bitten by a snake
Which of the following is a practical application of probability in the insurance industry?
Which of the following is a practical application of probability in the insurance industry?
Which method of assigning probability relies primarily on laws and rules?
Which method of assigning probability relies primarily on laws and rules?
Machine A produces 40% of a product and 10% of Machine A's products are defective. If a product is randomly selected, what is the probability it is produced by Machine A and is defective?
Machine A produces 40% of a product and 10% of Machine A's products are defective. If a product is randomly selected, what is the probability it is produced by Machine A and is defective?
An inspector has rejected 10 out of the last 90 batches. Using the relative frequency of occurrence, what is the probability that the inspector will reject the next batch?
An inspector has rejected 10 out of the last 90 batches. Using the relative frequency of occurrence, what is the probability that the inspector will reject the next batch?
In the context of probability, which of the following best describes an 'experiment'?
In the context of probability, which of the following best describes an 'experiment'?
When rolling a die, which of these outcomes is considered an elementary event?
When rolling a die, which of these outcomes is considered an elementary event?
If you roll a pair of dice, what represents the sample space?
If you roll a pair of dice, what represents the sample space?
A supplier ships a lot of six parts to a company, three of which are defective. If the customer randomly selects two parts, what does the sample space help determine?
A supplier ships a lot of six parts to a company, three of which are defective. If the customer randomly selects two parts, what does the sample space help determine?
A car can be purchased with choices of Red, Silver, Black, or White color; Cash, Lease, or Finance purchase type; and Hybrid or Electric engine. Using the mn counting rule, how many total combinations are possible?
A car can be purchased with choices of Red, Silver, Black, or White color; Cash, Lease, or Finance purchase type; and Hybrid or Electric engine. Using the mn counting rule, how many total combinations are possible?
In a class of 180 students, you want to randomly select 5 students and give each a prize. Each student can receive multiple prizes. How would you calculate the total number of possible selections?
In a class of 180 students, you want to randomly select 5 students and give each a prize. Each student can receive multiple prizes. How would you calculate the total number of possible selections?
When is it most appropriate to use permutations?
When is it most appropriate to use permutations?
A small company with 20 employees needs to randomly select 6 for interviews about an employee satisfaction program. How do you calculate the number of different groups of six that can be selected?
A small company with 20 employees needs to randomly select 6 for interviews about an employee satisfaction program. How do you calculate the number of different groups of six that can be selected?
A Venn diagram is used to illustrate what?
A Venn diagram is used to illustrate what?
In set theory, what does the 'union' of two sets represent?
In set theory, what does the 'union' of two sets represent?
What does it mean when two events are considered 'mutually exclusive'?
What does it mean when two events are considered 'mutually exclusive'?
If A is an event, what does A' (A prime) represent?
If A is an event, what does A' (A prime) represent?
Given event A: rolling a die and getting an even number. What is the complementary event A'?
Given event A: rolling a die and getting an even number. What is the complementary event A'?
In the general law of addition, what does the term $P(X \cap Y)$ represent?
In the general law of addition, what does the term $P(X \cap Y)$ represent?
Given $P(A) = 0.10$, $P(B) = 0.12$, $P(C) = 0.21$, $P(A \cap C) = 0.05$, and $P(B \cap C) = 0.03$, calculate $P(A \cup C)$.
Given $P(A) = 0.10$, $P(B) = 0.12$, $P(C) = 0.21$, $P(A \cap C) = 0.05$, and $P(B \cap C) = 0.03$, calculate $P(A \cup C)$.
Given $P(A) = 0.10$ and $P(B) = 0.12$, and knowing A and B are mutually exclusive, find $P(A \cup B)$.
Given $P(A) = 0.10$ and $P(B) = 0.12$, and knowing A and B are mutually exclusive, find $P(A \cup B)$.
68% of U.S. households own a pet and 31% of U.S. households have trouble paying energy bills. 17% own a pet and have trouble paying energy bills. What is the probability that a U.S. household owns a pet OR has trouble paying energy bills?
68% of U.S. households own a pet and 31% of U.S. households have trouble paying energy bills. 17% own a pet and have trouble paying energy bills. What is the probability that a U.S. household owns a pet OR has trouble paying energy bills?
Using the values in the joint probability table, what type of probability does the value in a single cell represent?
Using the values in the joint probability table, what type of probability does the value in a single cell represent?
Marginal probability focuses on calculating the probability of:
Marginal probability focuses on calculating the probability of:
Which of the following describes conditional probability?
Which of the following describes conditional probability?
Determine the formula for conditional probability:
Determine the formula for conditional probability:
When are two events X and Y considered independent?
When are two events X and Y considered independent?
In a population, 47% are female and 27% of working females work part-time. What is the probability that a randomly selected person from the Canadian workforce is a female working part-time?
In a population, 47% are female and 27% of working females work part-time. What is the probability that a randomly selected person from the Canadian workforce is a female working part-time?
Which of the following statements best defines Bayes' Rule?
Which of the following statements best defines Bayes' Rule?
A drug is produced by two companies: P (65%) and B (35%). Users of P experience side effects 8% of the time, while users of B experience side effects 12% of the time. If a user experiences side effects, what is the probability they used the drug from company P?
A drug is produced by two companies: P (65%) and B (35%). Users of P experience side effects 8% of the time, while users of B experience side effects 12% of the time. If a user experiences side effects, what is the probability they used the drug from company P?
Alex incorrectly fills 20% of orders, Alicia incorrectly fills 12%, and Juan incorrectly fills 5%. Alex fills 30% of all orders, Alicia fills 45%, and Juan fills 25%. If an order is filled incorrectly, what is the probability Alicia filled it?
Alex incorrectly fills 20% of orders, Alicia incorrectly fills 12%, and Juan incorrectly fills 5%. Alex fills 30% of all orders, Alicia fills 45%, and Juan fills 25%. If an order is filled incorrectly, what is the probability Alicia filled it?
In a study, 42% of consumers find credit cards safest for online purchases; none find both credit and debit cards safest, and 47% selected neither. What's the probability a respondent selected credit card but not debit card as safest?
In a study, 42% of consumers find credit cards safest for online purchases; none find both credit and debit cards safest, and 47% selected neither. What's the probability a respondent selected credit card but not debit card as safest?
What is the probability that a respondent selected Debit card?
What is the probability that a respondent selected Debit card?
What is the probability that a respondent selected debit card, given that the respondent selected credit card as safest for online purchases among TSYS study respondents?
What is the probability that a respondent selected debit card, given that the respondent selected credit card as safest for online purchases among TSYS study respondents?
According to the TSYS study findings, what is the probability that a person did not choose Credit Card, given that they did not choose Debit Card?
According to the TSYS study findings, what is the probability that a person did not choose Credit Card, given that they did not choose Debit Card?
Flashcards
What is Probability?
What is Probability?
A measure of how likely an event is to occur, varying from 0 (impossible) to 1 (certain).
The Classical Method
The Classical Method
A method of assigning probabilities based on established laws and rules, assuming all outcomes are equally likely.
Relative Frequency Method
Relative Frequency Method
Determining probabilities based on accumulated historical data (relative frequency of past occurrences).
What is an Experiment?
What is an Experiment?
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What is an Event?
What is an Event?
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Elementary Event
Elementary Event
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What is a Sample Space?
What is a Sample Space?
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The 'mn' Counting Rule
The 'mn' Counting Rule
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Sampling with Replacement
Sampling with Replacement
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What are Permutations?
What are Permutations?
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What is a Venn Diagram?
What is a Venn Diagram?
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What is a Union?
What is a Union?
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What is an Intersection?
What is an Intersection?
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Mutually Exclusive Events
Mutually Exclusive Events
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What is the Complement of A?
What is the Complement of A?
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Joint Probability
Joint Probability
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Conditional Probability
Conditional Probability
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What are Independent Events?
What are Independent Events?
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What is Bayes' Rule?
What is Bayes' Rule?
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Study Notes
Probability: BUS 232, Week 4, Chapter 4
- In 2016, Statistics Canada reported approximately 230,000 Canadians were granted a degree.
- Of these, 68,247 were males with basic degrees, and 105,549 were females with basic degrees, totaling 173,796.
- 19,422 males received Master's degrees, compared to 28,836 females, totaling 48,258.
- Doctoral degrees were awarded to 2,868 males and 2,850 females, amounting to 5,718.
Application of Probability
- Probabilities are used by insurance companies to set specific rates and coverage.
- Gaming industries use probability values to establish charges and payoffs.
- Human resources departments compare proportional breakdowns of employees by ethnicity, gender, age, etc., to the proportions in the general population.
Methods of Assigning Probabilities
- Classical Method: Probabilities are assigned based on laws and rules
- Relative Frequency of Occurrence Method: Probabilities are based on cumulated historical data
- Subjective Probability: Probabilities are subjective
Classical Method of Assigning Probabilities
- Probabilities are assigned based on laws and rules.
- Probabilities can be determined a priori, before the experiment.
- P(E) = ne/N, where N is the total possible outcomes of the experiment, ne is the number of outcomes in which the event occurs
- The probability will always be between 0 and 1
Experiment
- Experiment: Rolling a die
- Events: Roll a 1, Roll an Even Number, or Roll a number more than 3.
Elementary Events
- Cannot be decomposed or broken down into other events, denoted by lowercase letters.
- Example includes rolling a die and getting specific values.
Rolling a Pair of Dice
- The process involves possible elementary events
- A possible elementary event is 36
Sample Space
- Complete listings of all elementary events for an experiment.
Counting Possibilities: the mn counting rule
- This rule helps to count the amount of possibilities in an given experiement
- Multiply the total amount of possibilities for both events
- Example is purhcasing a car
Counting the Possible Sequences
- The number of sequences in a set are called permutations
Counting the Possible Sequences: population with replacement
- Randomly select a person from a poulation and allow them to be picked more than once
Venn Diagrams
- Compete an illustration that uses circles to show the relationships
Unions and Intersections
- Union: combines elements from both sets.
- Intersection: identifies the elements common to both sets.
Mutually Exclusive Events
- The occurrence of one event prevents the occurrence of another.
- Example: the occurance of heads makes tails impossible
Complementary Events
- The complement of event A, denoted A', includes all outcomes not in A.
- P(A') = 1 - P(A).
Complement of a Union
- Neither X nor Y involves events outside of both sets X and Y.
Addition Laws
- General Law of Addition: P(X∪Y) = P(X) + P(Y) - P(X∩Y)
- Special Law of Addition: applies to mutually exclusive sets.
Four Types of Probabilities
- Marginal Probability: The probability of 'X' occurring.
- Union Probability: The probability of 'X' or 'Y' occurring.
- Joint Probability: The probability of both 'X' and 'Y' occurring.
- Conditional Probability: The probability of 'X' occurring given 'Y' has occurred.
Conditional Probabilities
- The conditional probability of X occurring given that Y is known or has occurred is expressed as P(X|Y).
- Law of Conditional probability: P(X|Y) = P(X ∩ Y) / P(Y)
- General Law of Multiplication: P(X ∩ Y) = P(X) * P(Y|X) = P(Y) * P(X|Y)
Independent Events
- The occurrence or non-occurrence of one event does not affect the other event.
Multiplication Laws
- General Law of Multiplication: used to find the joint probability.
- Formula: P(X ∩ Y) = P(X) * P(Y|X) = P(Y) * P(X|Y)
- Special Law of Multiplication: Applies to independent events.
Bayes' Rule
- A formula that extends the use of the law of conditional probabilities to allow revision of original probabilities.
- P(Xi|Y) = [P(Xi) * P(Y|Xi)] / [P(X1) * P(Y|X1) + P(X2) * P(Y|X2) + ... + P(Xn) * P(Y|Xn)]
- Recall the Law of Conditional Probability: P(Xi|Y) = [P(Xi) * P(Y|Xi)] / P(Y)
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Description
Explore probability in BUS 232, Week 4, Chapter 4. Learn how probabilities are applied, especially by insurance companies and in gaming. Discover assigning probabilities such as classical, relative frequency, and subjective methods.
