Class Notes
(809,569)

Canada
(493,754)

University of Alberta
(12,938)

Statistics
(237)

STAT151
(146)

Paul Cartledge
(23)

Lecture

# Ch5.pdf

Unlock Document

University of Alberta

Statistics

STAT151

Paul Cartledge

Fall

Description

5.1 Introducing Probability
Def’n: An experiment is a process that, when performed, results in one and only one of
many observations.
These observations are called the outcomesof the experiment.
Probability is a numerical measure of likelihood that a specific outcome occurs.
3 Conceptual Approaches to Probability:
1) Classical probability
- equally likely outcomes exist when two or more outcomes have the same probability
of occurrence
- classical probability rule:
P(A) = (# of outcomes favourable to A) / (total # of outcomes for experiment)
2) Relative frequency concept of probability
- experiment repeated n times to simulate probability
- relative frequencies are NOT probabilities, they only approximate them.
- Law of Large Numbers: If an experiment is repeated again and again, the prob. of an
event obtained from the relative frequency approaches the actual or theoretical prob.
3) Subjective probability
- subjective probability is the degree of belief that an outcome will occur, based on the
available information
5.2/5.3 Calculating Probability
Def’n: A sample space (a.k.a. S) is the set of all outcomes of an experiment.
evennt (a.k.a. A) is a subset of elementary outcomesA ⊂ S.
Æ P(A) = probability that A occurs
• A union of 2 events is denoted by A or B (or AU B).
• An intersection of 2 events is denoted by A and B (or AI B).
C
• A complement of an event is denoted by A .
A Venn diagram is a picture that depicts S (events above drawn in class).
Experiment Outcomes Samapcle
Toss a coin Head, Tail S = { H, T }
Toss 2-headed coin Head S = { H }
Toss a $5 bill Get it back, Lose money S = { Lucky, Not Smart }
Pick a suit Spades, Clubs, Diamonds, Hearts S = { Sp, C, D, H }
(Associated Venn diagrams drawn in class)
Properties for calculating probabilities:
1. 0 ≤ P(A) ≤ 1
2. P(A) is the sum of probabilities of all elementary outcomes comprising A.
3. P(S) = 1 Basic Rules for Finding Probability of a Pair of Events:
Table 5X0 – 2-way table of responses
Hockey Like Indifferent Dislike Hockey Total
(A) (B) (C)
Male (M)
Female (F)
Total
Def’n: Marginal probability is the probability of a single event without consideration of
any other event.
Ex5.1) P(M) = P(F) =
P(A) = P(B) = P(C) =
Conditionalbility is the probability that an event will occur given that
another event has already occurred. If A and B are 2 events, then the conditional
probability of A given B is written as P(A | B).
P(A| B) = P(AI B) and P(B | A) =P(BI A)
P(B) P(A)
such that P(A) ≠ 0 and P(B) ≠ 0.
Ex5.2) P(like hockey | male) = P(A and M) / P(M) =
P(female | indifferent) = P(F and B) / P(B) =
Disjoint events are events that cannot occur together.
caddex5.5.4)
R = get red suit = {diamond, heart} E = even = {2, 4, 6}
B = get black suit = {spade, club} O = odd = {1, 3, 5}
F = get face card = {jack, queen, king} Pr = prime = {2, 3, 5}
Which pairs are disjoint?
Two events are independent if the occurrence of one does not affect the
probability of the occurrence

More
Less
Related notes for STAT151