Chapter 6 - Probablity

Question 0

A phenomenon is random if…

Answer 0

…if individual outcomes are uncertain but there is predictable behaviour in a large number of repetitions.

Question 1

Definition of probability

Answer 1

The proportion of times the outcome would occur in a very long (infinitely long) series of repetitions.

Question 2

Independent trials (or repetitions)

Answer 2

Repetitions or trails are said to be independent if the outcome of one trail does not affect the outcome of another
-ex a coin toss

Question 3

Three parts of a probability model

Answer 3

1. The sample space (S)
2. A list (Ę) of all possible events (E)
3. A way of assigning probabilities to events

Question 4

A n B

Read A and B

Answer 4

The intersection of two events A and B is the collection of outcomes that are both A and B

Question 5

A u B

Read A or B

Answer 5

The union of two events A and B is the collection of outcomes that are either A or B (or both).

Question 6

A-bar

Read: not A

Answer 6

The complement of an event A is the collection of outcomes not in A, denoted A-bar

Question 7

Four basic rules of the probability model 
Notation P(E) for probability of event E

Answer 7

1. For any event E, 0< P(E) <1
2. P(S) =1 (something must happen)
3. For any event E, P(E-bar)= 1-P(E)
4. Two events are disjoint if they have no common outcomes. See addition rule.

Question 8

Addition rule

Answer 8

If A and B are disjoint, then P(A or B) = P(A u B) = P(A) + P(B)

Question 9

General addition rule

Answer 9

P(A u B) = P(A) + P(B) - P(A n B)

Question 10

Events A and B are independent if…

Answer 10

…if knowing one had occurred doesn’t tell you anything about whether the other will or not

Question 11

The general multiplication rule:

Answer 11

P(A n B) = P( A | B) x P(B)

P(A n B) = P(B | A) x P(A)

Read P(A|B) as A given B

Question 12

Read P(A|B) as A given B

Answer 12

In general knowing B has happened may modify the probability of A; ie the conditional probability of A given B may not be the probability of A.

Question 13

The general multiplication rule from the definition of conditional probabilities:

Answer 13

P(A|B) = P(A n B)/P(B)

P(B|A) = P(A n B)/P(A)

Eg. For P(B|A) restricting to A the probability of B is the proportion of outcomes in A that are also in B

Question 14

bayes therom

Answer 14

Connects conditional probabilities

Is a long equation found in green book