Unit 4 - Probability and Discrete Distributions

Question 1

Define random

Answer 1

if individual outcomes are uncertain but there is a regular distribution of outcomes in a large number of repetitions

Question 2

Define probability

Answer 2

the proportion of times the outcome would occur in an infinitely long series of trialss

Question 3

What its the 2 components of the probability model?

Answer 3

• list of possible outcomes

- a probability for each outcome

Question 4

Define sample space (S)

Answer 4

set of all possible outcomes

Question 5

Define event

Answer 5

any subset of outcomes in the sample space

Question 6

How do you calculate the probability of an event A?

Answer 6

P9A) = # of outcomes in A/ # of outcomes in S

Question 7

Define intersection

Answer 7

all outcomes contained in both A and B (also includes the probability that both events occur simultaneously)

Question 8

What is the symbol of intersection of events?

Answer 8

A ∩ B

Question 9

Define union

Answer 9

consists of all outcomes that are contained in at least one of the events A OR B (included the probability that they both occur)

Question 10

What is the symbol of union of events?

Answer 10

A ∪ B

Question 11

What is a way of calculating the probability of the union of two events?

Answer 11

P(A∪B) = P(A) + P(B) - P(A∩B)

Question 12

When are two events are said to be mutually exclusive/disjoint?

Answer 12

if they have no outcomes in common

A ∩ B = Ø

Question 13

What does Ø mean?

Answer 13

empty set, set containing no outcomes

Question 14

When are 2 events said to be mutually exclusive?

Answer 14

if and only if P(A and B) = 0

Question 15

What is the equation of calculating when 2 events are mutually exclusive?

Answer 15

P(A∪B) = P(A) + P(B)

Question 16

Define exhaustive

Answer 16

if they together contain all the outcomes in S

Question 17

What is the complement of an event A?

Answer 17

the event consisting of all outcomes in the sample space which are not contained in A

Question 18

What is the symbol of complements?

Answer 18

A^c

Question 19

What is the probability of complements?

Answer 19

P(A^c) = 1 - P(A)

Question 20

When are 2 events said to be complements?

Answer 20

if they are both mutually exclusive and exhaustive of the sample space

Question 21

Define conditional probability

Answer 21

the probability that the event A occurs, given that an event B has occurred

Question 22

What is the symbol of conditional probability

Answer 22

P(A|B)

Question 23

How do you calculate P(A|B)?

Answer 23

P(A|B) = P(A∩B)/P(B)

Question 24

What its the definition of conditional probability (probability of intersections)?

Answer 24

P(A∩B) = P(A)P(B|A) = P(B)P(A|B)

Question 25

By the definition of conditional probability, what is the the probability of P(C|A∩B)?

Answer 25

P(C|A∩B) = P(A∩B∩C)/P(A∩B)

Question 26

What is the equation if two events A and B are said to be independent?

Answer 26

P(B|A) = P(B)
or
P(A|B) = P(A)

Question 27

A and B are independent if and only if what?

Answer 27

P(A∩B) = P(A)P(B)

Question 28

3 steps to find the probability of an event

Answer 28

1) list all outcomes contained in the event
2) find the probability of each of these outcomes
3) add these probabilities