UNIT 3

What is the formula for probability?

What is sample space and what is it denoted by?

all possible outcomes

denoted by S

What is an event and what is it denoted by?

all favorable outcomes

denoted by A, B, C..

The probability of an event A must be greater than or equal to __ or less than or equal to __. AKA:  __ ≤ P(A) ≤ __

0, 1

The probability of all outcomes sum to __. AKA: P(S) = __

1

If the probability of an event is 0, then the event is _________.

If the probability of an event is 1, then the event is _________.

impossible, certain

What is the complement of an event?

everything NOT in the event of interest

What is the notation for the complement of an event?

What is the formula for complement of an event?

What is the intersection?

all elements that belong to BOTH the events of interest

What is the notation for the intersection?

What are key words/phrases for intersection?

• both

• happening at the same time

• simultaneously

• joint occurrence

What does the law of total probability state?

What is the union?

ALL the elements that belong to ALL the events of interest

What is the notation for union?

What are key words/phrases for union?

• or

• either

• at least

• all together

What is the formula for union?

Name the 2 statements of DeMorgan’s Law.

What are mutually exclusive events?

two events that CANNOT occur together

What is the formula for mutually exclusive events?

P(A ∩ B) = 0

What are independent events?

the occurrence of one event does NOT affect the occurrence of the other

What is the formula for independent events?

P(A ∩ B) = P(A) P(B)

What is the formula for joint probabilities according to the diagram?

What do joint probabilities describe?

how often that combination of two variables occur

What are the key phrases for joint probabilities?

• and

• together

• both

What is the formula for marginal probabilities according to the diagram?

What do marginal probabilities describe?

how often one variable occurs

What are key phrases for marginal probabilities?

one variable is mentioned

What is the formula for conditional probabilities according to the diagram?

What do conditional probabilities describe?

what is the proportion/percentage of one variable, given a specific value of the other category

What are the key phrases for conditional probabilities?

• given

• of those two

• assuming

What is the notation used to represent conditional probabilities?

P(A | B) OR P(B | A)

What is the other formula for calculating conditional probabilities?

What is the formula for expected value (mean)?

What is the formula for variance of a probability?

What is the acronym for binomial probability distributions and what does it stand for?

Binary -> one of two outcomes

Independent -> the results of one trial does not affect the result of another

Number fixed -> fixed number of trials

Same probability-> constant p

What is the binomial probability distribution function?

What is the formula for expected value (mean) of binomial probability distributions?

E(X) = np

What is the formula for variance of binomial probability distributions?

Var(X) = np(1 - p)

What does a density curve describe?

the overall pattern of a distribution

The area under the density curve is ALWAYS equal to __.

1

The density curve is always _____ the x axis.

above

The area between two values under the density curve tells us.. (3)

• the proportion of values that fall in that range

• the probability of being between the two values

• multiply by 100 to get the percentage

Complete the following notations.

The shape of a normal density curve can be described as ______, _________ and _______.

bell-shaped, symmetric & unimodal

If X is normally distributed, we write ______.

Fill in the blank and straw what each character means.

E.G. X ~ N (0,1)