Chapter 3 Flashcards
Why study probability?
Gives us a way to evaluate risks associated with just about any sort of behavior
What is probability?
Key to accessing and understanding risks involved in any decision-making process
How do social scientists use probability?
Assess the likelihood of making incorrect inferences when generalizing about human behavior
What is probability in simple terms?
Likelihood of an event expressed in numerical terms as a fraction, decimal, or percent
What does a probability of zero indicate?
The event will never happen
What does a probability of one indicate?
It will absolutely happen
What values can’t be a probability?
A negative number
What is a probability experiment?
A situation involving chance or probability that leads to observable and measurable results
How many trials could a probability experiment consist of?
One or many trials
How many outcomes come from each trial?
Only one outcome for each trial
What do all probability experiments have in common?
Must have more than one possible outcome, can be specified in advance, due to chance
What is a non-example of probability?
Only has one possible outcome, can’t be specified in advanced, and outcomes are not due to chance
What are examples of non-probability?
Football player running for a touchdown, buying a raffle ticket, your church sponsoring a Vegas night to raise money for charity
What is a trial?
Single performance of a probability event
What is an outcome?
The result of a single probability experiment
What is a set?
Describe collections of objects or values that have been defined according to a rule or statement
What is each object or value in a set?
An element of the set
What are sets denoted by?
A capital letter
What is an event?
Subset of the sample space, collection of all possible outcomes of a probability experiment
What does a simple event consist of?
Single outcome
What does a compound event consist of?
More than one outcome
What is the sample space?
Description of all possible outcomes of a probability experiment
What is the first step in determining the probability of any single outcome?
Writing out the description of the sample space
What does the sum of all probabilities of all possible outcomes in the sample space must equal to?
One
What is the formula for any given outcome?
P(x) = X / Total outcomes in the sample space
What is the complement of an event?
All outcomes that are not the event
What happens if the complement of an event is not occurring?
Designated as a prime
What can the relationship for complement of events be shown as?
P(A’) = 1- P(A)
How can you find the probability associated with a prime number?
Take 1 and subtract that from the sample space value then that is the value of the prime complement value
What are the three ways to arrive at a probability statement?
Theoretical probability, empirical probability, and subjective probability
What is theoretical or classical probability?
Assumption about the nature of the event, assumed that n events are equally likely to occur
What is empirical or relative frequency probability?
Based on the observed outcomes of one or a series of trials
What type of probability is used most often in statistical inference procedures?
Empirical
What is subjective probability?
Based on personal belief about the likelihood of an event occurring
What is subjective probability not based on?
Any real math or formal calculations, and is therefore unreliable
How would you represent the event of choosing a specific result?
P(E) = P(D) = Probability
How would you represent if an event is equally likely?
P(A) + P(B) + P(C) + P(D) = . + . + . + . = 1 (should add up to one)
What are the four types of events in probability experiments?
Independent events, dependent events, mutually exclusive events, complementary events
What happens if two events are independent?
Probability that one will occur is not affected by whether or not the other has occurred
What is an example of independent events?
If you roll a dice twice the outcome of the second trial is not affected by the outcome of the first trial so it would still be 1/6
What are dependent events?
Probability that one will occur is affected by the occurrence of the other
What is an example of a dependent event?
If a queen is drawn from a deck of cards and the card is not replaced then the probability of drawing a queen on the second trial is changed as a result of the outcome of the first trial
What are mutually exclusive events?
If two events cannot occur at the same time
What is an example of a mutually exclusive event?
Cramming for an exam and training for a bicycle race
What does the Upside down U symbol indicate?
An intersection between point A and B
What happens if two events have a non-zero chance of occurring?
The can’t be independent if mutually exclusive
What happens if two events are independent?
They can’t be mutually exclusive
What are not mutually exclusive events?
If they can occur at the same time
What is an example of a not mutually exclusive event?
If there are juniors and English majors you can be both
What are complementary events?
Two outcomes of a trial that are the only two possible outcomes
What do complementary events imply?
That the events are mutually exclusive since only one of the other two outcomes can occur
What is a example of a complementary event?
Flipping a coin and getting head for tails are complementary outcomes because there are no other outcomes possible, the result must be one or the other
What does the relationship between complementary and mutually exclusive events indicate?
That all complementary events are mutually exclusive but not all mutually exclusive events are necessarily complementary
What is the fundamental counting principle?
Enables us to find the number of ways a combination or series of independent events can occur
What can the fundamental counting principle be used to quickly determine?
Total possible outcomes in a sample space without having to create a diagram
What is the multiplication rule?
Can be used to find the probability that two or more events occurs in sequence and takes the fundamental counting principle a step further by taking into account both independent and dependent events
How can you simple calculate the fundamental counting principle?
Taking the possible outcomes and then putting that to the power of how many times it is being funneled through 10 possible numbers through a 4 digit code is 10^4
What happens in the multiplication rule if there are independent events?
Probability that they will all occur is equal to the product of their individual probabilities
How can the independent events application of the multiplication rule be represented?
P (A and B) = P(A) x P (B) —can be expanded for as many events as you need to multiply
My process for explaining the independent multiplication process
Taking the probabilities of however many events you are looking at and then you take those calculated probabilities and multiply them together to get your combined value for the independent events
How can dependent events be represented in the context of the multiplication rule?
Probability of event B occurring, given that event A has already occurred
What is dependent events in the multiplication rule represented by?
P (B | A)
What is the first step in the dependent event probability process?
Determine the probability that A will occur P(A)
What is the second step in the dependent event probability process?
Determine the probability that B will occur, given that A has occurred P (B | A)
What is the third step in the dependent event probability process?
Multiple P(A) by P(B|A) to find the probability that events A and B will occur in sequence
What is the representation of step three in the dependent event process?
P (A and B) = P(A) x P(B|A)
Description of the process of dependent events in my words
You take the initial probability of your first event, then you take the probability of the second event, before you multiple the two together and that’s your combined probability
What is the addition rule?
Be used to find the probability that at least one of the two events will occur
How does the addition rule differ from the multiplication rule?
Multiplication rule is used to find the probability that both or all events will occur, addition rule is used to find probability that either event will occur
What can you think of the addition rule as?
Or
What can you think of the multiplication rule as?
And
What is the basic statement of the addition rule stated as?
P(A and B)= P(A) + P(B) - P(A and B)
What are mutually exclusive events in the addition rule?
Probability that one or the other will occur is equal to the sum of their individual probabilities
How can mutually exclusive events in the addition rule be stated as?
P(A and B) = P(A) + P(B)
What is the process of the mutually exclusive events in the addition rule in my words
Take the probability of event one and event 2 and then add them together to get the final result
What is the not mutually exclusive events of the addition rule?
If they are not mutually exclusive we have to subtract the probability associated with the intersection of the events to avoid double counting the shared elements
What is the process of not mutually exclusive events in my own words in regard to the addition rule?
Take the probabilities of your first probability and the second probability and then the probability of the common connector. You then take the original two values and subtract them from the common connector to get your final probability
What is the role of sample space in a probability experiment?
collection of all the possible outcomes
What does calculating probabilities allow us to predict?
Likelihood of events over the long term
What are the equally-likely models of probability?
Any one event in the sample space is just as likely to occur as any other possible event
What is random sampling?
Techniques ensure that all possible samples of a particular size have an equal chance of being selected from a population
What is sampling with replacement?
Any one observation can appear more than once in a sample
What is sampling without replacement?
Any observation can appear only once in a sample
When is the additive theorem easiest to use?
When the events are mutually exclusive
When is the multiplicative theorem easiest to use?
When the events are independent
