Podcast
Questions and Answers
Which of the following best describes the core idea of probability?
Which of the following best describes the core idea of probability?
- A complex calculation involving only past events.
- An absolute guarantee of an event's outcome.
- A method for precisely predicting future events.
- A numerical measure of the likelihood that an event will occur. (correct)
Which of the following is the most accurate description of an experiment in the context of probability?
Which of the following is the most accurate description of an experiment in the context of probability?
- A process that generates well-defined outcomes. (correct)
- A random process without structured results.
- A process with unpredictable outcomes.
- A process with only one possible outcome.
In the context of counting rules, what is a multiple-step experiment?
In the context of counting rules, what is a multiple-step experiment?
- An experiment that is repeated multiple times.
- An experiment described as a sequence of steps. (correct)
- An experiment with only two possible outcomes.
- An experiment performed with a single action.
Kentucky Power & Light is starting a project with two stages: design and construction. The design stage can take 2, 3, or 4 months, and construction can take 6, 7, or 8 months. How many possible completion time outcomes are there?
Kentucky Power & Light is starting a project with two stages: design and construction. The design stage can take 2, 3, or 4 months, and construction can take 6, 7, or 8 months. How many possible completion time outcomes are there?
What differentiates combinations from permutations when counting experimental outcomes?
What differentiates combinations from permutations when counting experimental outcomes?
An inspector needs to select 3 parts out of 8 for inspection. In how many ways can this selection be made if the order of selection does not matter?
An inspector needs to select 3 parts out of 8 for inspection. In how many ways can this selection be made if the order of selection does not matter?
What are the two basic requirements for assigning probabilities to experimental outcomes?
What are the two basic requirements for assigning probabilities to experimental outcomes?
In assigning probabilities, when is the classical method most appropriate?
In assigning probabilities, when is the classical method most appropriate?
When is the 'relative frequency' method most suitable for assigning probabilities?
When is the 'relative frequency' method most suitable for assigning probabilities?
When is the 'subjective method' used to assign probabilities?
When is the 'subjective method' used to assign probabilities?
What is the complement of an event?
What is the complement of an event?
If the probability of event A is 0.3, what is the probability of the complement of A?
If the probability of event A is 0.3, what is the probability of the complement of A?
What does the addition law of probability help determine?
What does the addition law of probability help determine?
Events A and B are mutually exclusive. If P(A) = 0.4 and P(B) = 0.3, what is P(A ∪ B)?
Events A and B are mutually exclusive. If P(A) = 0.4 and P(B) = 0.3, what is P(A ∪ B)?
In probability theory, what are mutually exclusive events?
In probability theory, what are mutually exclusive events?
What does conditional probability measure?
What does conditional probability measure?
Given events A and B, if P(A ∩ B) = 0.2 and P(B) = 0.5, what is P(A|B)?
Given events A and B, if P(A ∩ B) = 0.2 and P(B) = 0.5, what is P(A|B)?
Which of the following statements about probability is most accurate?
Which of the following statements about probability is most accurate?
In the Monty Hall problem, after you pick a door, the host opens another to reveal a goat. Should you switch doors?
In the Monty Hall problem, after you pick a door, the host opens another to reveal a goat. Should you switch doors?
A company has 2 assembly lines. Line A produces 60% of the products, with a 4% defect rate. Line B produces 40% with a 2% defect rate. What is the overall probability that a randomly selected item is defective?
A company has 2 assembly lines. Line A produces 60% of the products, with a 4% defect rate. Line B produces 40% with a 2% defect rate. What is the overall probability that a randomly selected item is defective?
A weather forecaster states that there is a 70% chance of rain tomorrow. What type of probability assignment is this?
A weather forecaster states that there is a 70% chance of rain tomorrow. What type of probability assignment is this?
In a class of 30 students, 12 are taking statistics, 8 are taking calculus, and 3 are taking both. What is the probability that a randomly selected student is taking either statistics or calculus?
In a class of 30 students, 12 are taking statistics, 8 are taking calculus, and 3 are taking both. What is the probability that a randomly selected student is taking either statistics or calculus?
In a game, a player rolls a fair six-sided die. What is the probability of rolling an even number?
In a game, a player rolls a fair six-sided die. What is the probability of rolling an even number?
When rolling two fair six-sided dice, what is the probability of obtaining a sum of 7?
When rolling two fair six-sided dice, what is the probability of obtaining a sum of 7?
A bag contains 5 red marbles and 3 blue marbles. If two marbles are drawn without replacement, what is the probability that both are red?
A bag contains 5 red marbles and 3 blue marbles. If two marbles are drawn without replacement, what is the probability that both are red?
What is the formula for computing permutations?
What is the formula for computing permutations?
What is the formula for computing combinations?
What is the formula for computing combinations?
In a survey, 60% of people prefer coffee, and 40% prefer tea. Of those who prefer coffee, 70% add sugar. Of those who prefer tea, 30% add sugar. What percentage of all people add sugar to their drink?
In a survey, 60% of people prefer coffee, and 40% prefer tea. Of those who prefer coffee, 70% add sugar. Of those who prefer tea, 30% add sugar. What percentage of all people add sugar to their drink?
A box contains 10 items, 3 of which are defective. If two items are selected at random without replacement, what is the probability that neither item is defective?
A box contains 10 items, 3 of which are defective. If two items are selected at random without replacement, what is the probability that neither item is defective?
A company employs 50 people. 30 have a college degree, and 12 have professional certifications, and 5 have both. If an employee is selected at random, what's the probability they have neither a degree nor a certification?
A company employs 50 people. 30 have a college degree, and 12 have professional certifications, and 5 have both. If an employee is selected at random, what's the probability they have neither a degree nor a certification?
If two events A and B are independent, then:
If two events A and B are independent, then:
What is the probability of drawing an ace from a standard deck of 52 cards?
What is the probability of drawing an ace from a standard deck of 52 cards?
A game involves spinning a wheel divided into 20 equal sections, numbered 1 to 20. What is the probability that the wheel will stop on a number that is both even and a multiple of 5?
A game involves spinning a wheel divided into 20 equal sections, numbered 1 to 20. What is the probability that the wheel will stop on a number that is both even and a multiple of 5?
A pharmaceutical company is testing a new drug. In clinical trials, 65% of patients showed improvement, 15% experienced side effects, and 8% showed improvement and experienced side effects. What is the probability that a patient showed improvement or experienced side effects?
A pharmaceutical company is testing a new drug. In clinical trials, 65% of patients showed improvement, 15% experienced side effects, and 8% showed improvement and experienced side effects. What is the probability that a patient showed improvement or experienced side effects?
A survey found that 80% of customers like pizza, 70% like burgers, and 55% like both. What percentage of customers like either pizza or burgers?
A survey found that 80% of customers like pizza, 70% like burgers, and 55% like both. What percentage of customers like either pizza or burgers?
In a certain city, 60% of the days are cloudy. What is the probability that a randomly selected day is not cloudy?
In a certain city, 60% of the days are cloudy. What is the probability that a randomly selected day is not cloudy?
A company sends out two teams to solicit donations. Team A visits 40% of the households and Team B visits the rest. Team A gets a donation from 5% of the households they visit, while Team B gets a donation from 8%. What is the overall percentage of households that donate?
A company sends out two teams to solicit donations. Team A visits 40% of the households and Team B visits the rest. Team A gets a donation from 5% of the households they visit, while Team B gets a donation from 8%. What is the overall percentage of households that donate?
Flashcards
What is Probability?
What is Probability?
A numerical measure of how likely an event is to occur.
What is an experiment?
What is an experiment?
A process that generates well-defined outcomes.
What is the Multiple-Step Experiment Rule?
What is the Multiple-Step Experiment Rule?
If an experiment has k steps, with n1, n2, ..., nk possible outcomes respectively, the total number of experimental outcomes is (n1)(n2)...(nk).
What are Combinations?
What are Combinations?
Signup and view all the flashcards
What are Permutations?
What are Permutations?
Signup and view all the flashcards
Probability Requirement 1
Probability Requirement 1
Signup and view all the flashcards
Probability Requirement 2
Probability Requirement 2
Signup and view all the flashcards
What is Classical Method?
What is Classical Method?
Signup and view all the flashcards
What is Relative Frequency Method?
What is Relative Frequency Method?
Signup and view all the flashcards
Subjective Method
Subjective Method
Signup and view all the flashcards
What is the Complement of an Event?
What is the Complement of an Event?
Signup and view all the flashcards
Addition Law
Addition Law
Signup and view all the flashcards
What are Mutually Exclusive Events?
What are Mutually Exclusive Events?
Signup and view all the flashcards
Conditional Probability
Conditional Probability
Signup and view all the flashcards
Study Notes
- AE 09 (Lec) is the course code.
- Rocelle Ann G. Terco is the facilitator.
Learning Objectives
- Understand basic probability concepts.
- Learn various counting rules.
- Identify ways of assigning probabilities.
- Familiarize yourself with the basic relationships of probability.
Flow of Session
- Prelim Exam Review
- Intro to Probability
- Counting Rules
- Basic Relationships of Probability
- Conditional Probability
Probability Questions
- Possible questions include the chance of rain, stock increase, heart attack, living past 70, rolling dice doubles, winning the lottery, or becoming a billionaire.
Probability
- Probability is a numerical measure of the likelihood that an event will occur.
- Numerical probability ranges from 0-1.
Experiment
- An experiment is a process that generates well-defined outcomes.
- Experimental outcomes for tossing a coin are heads or tails.
- Experimental outcomes for selecting a part for inspection are defective or non-defective.
- Experimental outcomes for conducting a sales call are purchase or no purchase.
- Experimental outcomes for rolling a die are 1, 2, 3, 4, 5, 6.
- Experimental outcomes for playing a football game are win, lose, or tie.
- The sample space is all the possible outcomes from the experiment.
Multiple-Step Experiments
- If an experiment involves a sequence of k steps, with n1 possible outcomes on the first step, n2 on the second, and so on, the total number of experimental outcomes is (n1)(n2)...(nk).
Combinations
- Combinations allow counting the number of experimental outcomes when the experiment involves selecting r objects from a set of n objects.
- An inspector randomly selects 2 of 5 parts for inspection, there exist 10 possible ways this can happen.
- A,B,C,D, and E are possible combinations of selected parts.
- Ultra Lotto 6/58 is a Philippine Charity Sweepstakes Office (PCSO) where six numbers from 1-58 are chosen to play.
Permutations
- Permutations compute the number of experimental outcomes when the experiment involves selecting r objects from a set of n objects, where order is important.
- An inspector randomly selects 2 of 5 parts for inspection; there are 20 permutations of 2 parts can be selected.
Assigning Probabilities
- Each experimental outcome must be between 0 and 1, inclusively.
- The sum of the probabilities for all the experimental outcomes must be equal to 1.
Classical Method
- Appropriate when all experimental outcomes are equally likely.
Relative Frequency Method
- Data is available to estimate when an experimental outcome occurs with a large number of trials.
Subjective Method
- Appropriate when one cannot realistically assume that the experimental outcomes are equally likely and when little relevant data are available.
- An analyst estimates the S&P 500 will hit all-time highs at 20% the analyst evaluates trends and current market conditions.
Complement of an Event
- A purchasing agent states is 90% confidence a supplier will send a shipment that is free of defective parts, we can conclude that there is a 10% probability that the shipment will contain defective parts.
Addition Law
- At the end of a performance evaluation period, the production manager found that 5 of the 50 workers completed work late, 6 of the 50 workers assembled a defective product, and 2 of the 50 workers both completed work late and assembled a defective product, the probability of this happening is equal to 0.18%.
Mutually Exclusive Events
- Mutually Exclusive Events means that one or the other event will occur alone.
Conditional Probability
- This is the possibility of an event or outcome happening, based on the existence of a previous event or outcome.
- A survey of smartphone users showed that 47% use an iPhone. If 26% of iPhone users are under the age of 25 and 30% of non-iPhone users are under the age of 25, find the probability that someone does not use an iPhone given that the person is aged at least 25 years old.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
