Chapter 4: Probability

Question 1

Experiment

Answer 1

-an activity that has specific results that can occur, but it is unknown which results will occur

Question 2

Outcomes

Answer 2

• the results of an experiment

Question 3

sample space

Answer 3

-collection of all possile outcomes of the experiment, usually denoted as SS

Question 4

event

Answer 4

-a set of certain outcomes of an experiment that you want to have happen

Question 5

event space

Answer 5

-the set of outcomes that make up an event, this symbol is usually a capital letter

Question 6

simple event

Answer 6

-an event that consists of a single outcome
ex: tossing heads and rolling a 3
-an event that consist of more than one outcome is not a simple event
ex: tossing heads and rolling an even number

Question 7

Fundamental counting principle

Answer 7

-if one event can occur in m ways and a second event can occur in n ways, the number of ways the two events can occur in sequence is m*n
-can be extended for any nymber of events occuring in sequence

Question 8

classical (thoretical) probability

Answer 8

-each outcome in a sample space is equally likely
P(E) = number of outcomes in event E/ number of outcomes in sample space

Question 9

Empirical (statistical) probability

Answer 9

-based on observations obtained from probability experiments
-relative frequency of an event
P(E) = Frequency of event E/ total frequenct = f/n

Question 10

Law of large numbers

Answer 10

-an experiment is repeated over and over, the empirical probability of an event approaches the theoretical (actual) probability of the event
-as n increases, the relative frequency tends towards the actual probability value

Question 11

Theoretical probabilities

Answer 11

-not always feasible to conduct an experiment over and over. So it would be better to be able to find the probabilities without conducting the experiment, this is called theoretical probabilities
-an assumption you need to consider is that all of the outcomes in the sample space need to be equally likely outcomes. This means that every outcome of the experiment needs to have the same chance of happening
- P(A) = # of outcomes in event spaces/ # of outcomes in sample space

Question 12

certain event

Answer 12

-if the P (event) = 1, then it will happen and is called the certain event

Question 13

impossible event

Answer 13

-if the P(event) = 0, then it cannot happen and its caled this

Question 14

complement of event E

Answer 14

-the set of all outcomes in a sample space that are not included in event E
-denoted E’ (E prime)
P(E’) + P(E) = 1
P(E) = 1-P(E’)
P(E’) = 1- P(E)

Question 15

Mutual exclusivity

Answer 15

-two events are mutually exclusive if they can’t happen at the same time

Question 16

independence

Answer 16

-two events are independent if the fact that one happens does not alter the probability of the second happening

Question 17

Addition rules

Answer 17

-if two events A and B are mutuall exclusive then P(A or B) = P(A) + P(B) and P(A and B) = 0
-if two events are A and B are not mutually exclusive then P(A or B) = P(A) + P(B) - P(A and B)
-if two events A and B have a common element, you have to subtract it so

Question 18

Actual odds against event A occuring are the ratio

Answer 18

P (Ac)/ P(A) usually expressed in the form a:b or a to b, where a and b are intergers with no common factor

Question 19

Actual odds in favor even A occuring are the ratio

Answer 19

P(A)/ P(Ac) which is the reciprocal of the odds against. If the odds against A are a:b, then the odds in favor event A are b:a

Question 20

The payoff odds

Answer 20

-are againt event A occuring are the ratio of the net profit (if you win) to the amount bet
payoff odds against event A = (net profit) : (amount bet)

Question 21

Restricted sample space R

Answer 21

-probabilities calculated after information is given. This is where you want to find the probability of event A happening after you know that event B has happened, then you do not need to consider the rest of the sample space. You only need the outcomes that make up event B. Event B is the new sample space
-the event following the vertical line is always the restricted space

Question 22

Independent events

Answer 22

-the occurance of one of the events does not affect the probability of the occurence of the other event
- P (B|A) = P(B) or P(A|B) = P(A)
-events that are not independent are dependent

Question 23

Multiplication rule for the probability of A and B

Answer 23

-the probability that two events A and B will occur in sequence is
-P(A and B) = P(A) * P(B|A)
-for independent events the rule can be simplified to
-P(A and B) = P(A) * P(B)
-can be extended for any nymber of independent events

Question 24

Permutations

Answer 24

-an ordered arrangement of objects
-the number of different permutations of n distinct objects is n! (n factorial)
n! = n(n-1)(n-2)(n-3)… 32*1
- 0! = 1

Question 25

permutationss of n objects taken r at a time

Answer 25

-the number of different permutations of n distinct objects taken r at a time

Question 26

distinguishable permutations

Answer 26

0the number of distinguishable permutations of n objects where n1 are one type, n2 are of another type, and so on -when you have the same thing twice

Question 27

combinations

Answer 27

-a selection of r objects from a group of n objects without regard to order