01 Probability Flashcards
You __(v.)__ a coin (2 answers)
Toss; flip
♡♧♢♤ are the four __(n.)__ in a pack of __(n.)__
Suits in a pack of playing cards
The King, Queen, and Jack in a pack of cards are called the __(n.)__ cards
Face cards
⚂ is a __(n.)__
a die
⚂⚄ are __(n., pl.)__
dice (not dies)
You __(v.)__ a die
roll or throw
Random means…
- each individual outcome is unpredictable or uncertain
- there is a pattern over many repetitions
What is an experiment?
Any phenomenon with random results
What is the sample space, S, of an experiment?
The set of all possible outcomes
What is an event?
A subset of the sample space; a set of one or more possible outcomes
If A is an event, what is P(A)?
The probability of the event A occurring
What is the definition of the probability of an outcome?
The long-term relative frequency of the outcome; the proportion of times the outcome would occur in a long series of repetitions
What is the definition of experimental probability?
P(A) = the number of times the desired outcome occurs / the total number of trials
What is a trial?
A repetition of a phenomenon with random results.
For example, each roll of a die is a trial
What is a distribution?
The pattern of frequencies of the different possible outcomes to a random phenomenon
What is theoretical probability?
If there are k individual outcomes to an event, and each is equally likely, then the theoretical probability of each outcome is 1/k.
What is a fair/unbiased coin/die?
One in which each possible outcome is equally likely
A probability model consists of two parts; what are they?
- A sample space, S
- a means of assigning probabilities to events
What are the four suits in a pack of playing cards called?
- ♡ Hearts
- ♧ Clubs
- ♢ Diamonds
- ♤ Spades
What does it mean if events or trials are independent?
The outcome of one event or trial does not affect the outcome of any other event or trial.
What does it mean to say that two events are mutually exclusive or disjoint?
They cannot occur together;
eg “passing the exam” and “failing the exam” are disjoint events - it is not possible to both pass and fail the exam.
What does {A∪B} mean?
“A union B” is the set of all outcomes which are in either A or B (or both).
What does {A∩B} mean?
“A intersect B” is the set of all outcomes that are both A and B.
If A and B are mutually exclusive or disjoint, then we can say something about either {A∪B} or {A∩B}; what?
{A∩B} = ∅, or A intersect B is empty.
What is the General Addition Rule for P(A or B)?
P(A or B) = P(A∪B) = P(A) + P(B) - P(A∩B)
What is the multiplication rule for P(A or B) and when is it valid?
P(A or B) = P(A∩B) = P(A)⋅P(B),
if A and B are independent events.
What is conditional probability?
The situation where the probability of a second event is dependent on the outcome of a first event.
For example, the probability of the event “snow falls on a day” depends on the outcome of the event “the day is in winter.”
Conditional probability is defined as P(B|A) =…?
The probability of B given A,
P(B|A) = P(A∩B)/P(A).
If A and B are independent events, what can we say about them?
P(B|A) = P(B); the conditional probability of B given A is the same as the probability of B
also
P(A∩B) = P(A)⋅P(B)
How many different groups of size r can you make from n objects? (the order of the objects is not important)
- “n choose r” = nCr = n! / r!(n-r)!
- each of these groups is called a combination
How many different groups of size r can you make from n objects if the order of the objects is important?
- nPr = n! / (n-r)!
- each of these groups is called a permutation
What tool can you use to help you calculate probabilities in a complex situation?
A tree diagram
What is Benford’s law?
The distribution of the first digits of numbers in accounting records - the 9 possible first digits do not have equal probability of occurring; 1 is the most common first digit, then 2, then 3…
What are the 5 key facts to remember about probability?
- P(A) = number of desired outcomes / total number of trials
- independent events are events whose outcomes do not affect each other
- mutually exclusive events are events which cannot occur together
- P(A or B) = P(A) + P(B) - P(A and B)
- if A and B are independent, P(A and B) = P(A)⋅P(B)
