Transcript Chapter 14: Probability - Village Christian School

Chapter 5-2
The Idea of Probability
AP Statistics
Classical Definition

The probability of an event E, denoted
P(E), is:
# of outcomes favorable to E
P E 
# of outcomes in the sample space
 Note:
This method for calculating
probabilities is ONLY appropriate when the
outcomes of an experiment are equally
likely.
 For example, rolling a die or selecting a card
from a deck are experiments that have
equally likely outcomes.
The Relative Approach

When it’s difficult to find a probability,
sometimes we use a relative approach and an
alternate definition for probability:
# of times E occurs
P E 
# of trials
as the # of trials becomes very large
 From
P(3)?
a lopsided-die, how would we find the
# of times a 3 is rolled

total # of times the die is rolled
Forming New Events
Two events that have no outcomes in
common are said to be disjoint or
mutually exclusive.
 ex: Bobby Fisher and Borris Spassky are
playing chess:
 How many possible outcomes are there?

 There
are three possibilities…
 Bobby
Fisher winns, Borris wins, or there is a draw
(neither win).
 Can Bobby win if Borris wins?
 Can Borris win if Bobby wins?
 Can either win when there is a draw?
Probability

Venn Diagrams and Probabilities:
 How
do the Raiders Perform when it rains?
Worksheet
Basic Rules of Probability

Forming New Events

Let A and B denote 2 events:
The event not A consists of all experimental
outcomes that are not in event A. This event
is often called the complement of A.
2. The event A or B consists of all experimental
outcomes that are in at least one of the two
events, that is, in A, in B, or in both A and B.
This event is called the union of events A and
B
3. The event A and B consists of all experimental
outcomes that are in BOTH of the events A
and B. This event is called the intersection of
events A and B
1.
Examples

Find the probability of each of the following:
1.
2.
3.
4.


P(rolling a 6) = ?
P(rolling an even #) = ?
P(drawing the queen of spades) = ?
P(drawing any queen) = ?
Which of these events are simple events?
Here are some events where the outcomes are
not equally likely:

Letter grade on the next exam:


P(A) ≠ P(B) ≠ P(C) ≠ P(D) ≠ P(F) ≠ 1 / 5
If the probabilities are not equally likely, you cannot
use the classical definition.
The Relative Approach




What is the probability of drawing a face card if I
have a messed up collection of cards that
includes several decks that have been mixed
together with many of the cards missing?
If I were to draw a card from the scrambled deck,
what are the possible outcomes? Are they
equally likely??
How can I estimate P(face card)?
I can repeatedly draw cards and keep track of the
ratio:
# of face cards
P(face card) 
total # of cards drawn
Forming New Events

List all possible outcomes in the following
events:
A 
c
A B 
A B 
A B 
c
A A 
c