Download Lecture 22 - Probability

Probability
Lecture 22
Section 7.1 – 7.4.1
Wed, Oct 20, 2004
Random Outcomes

To have a random outcome, we must have a
procedure in which at least one step is left to
chance.
Select a student and see what is grade was on Test
#1.
 Wherein lies the randomness?


Sample space or outcome space – the set of all
possible outcomes of the procedure.
Random Outcomes


The various possible outcomes may be equally
likely, but they do not have to be.
Toss a coin.


Heads or tails.
Look out the window.
Hurricane or no hurricane.
 It depends on whether you live in Florida.

Example: Toss 2 Coins


Toss two coins and observe how each coin
lands.
Draw a tree diagram:
Example: Toss 2 Coins


Toss two coins and observe how each coin
lands.
Draw a tree diagram:
1st coin
H
T
Example: Toss 2 Coins


Toss two coins and observe how each coin
lands.
Draw a tree diagram:
2nd coin
1st coin
H
H
T
T
Example: Toss 2 Coins


Toss two coins and observe how each coin
lands.
Draw a tree diagram:
2nd coin
1st coin
H
H
T
T
H
T
Example: Toss 2 Coins


Toss two coins and observe how each coin
lands.
Draw a tree diagram:
1st coin
2nd coin
Sample
Space
H
HH
T
HT
H
TH
T
TT
H
T
Example: Toss 2 Coins

The sample space is the set
{HH, HT, TH, TT}.
Events




Event – a collection of possible outcomes.
Therefore, it is a subset of the sample space.
We say that the event occurs if the actual
outcome is among those included in the event.
Otherwise, the event does not occur.
Events




A Venn diagram is a convenient way to draw an
event.
Draw a rectangle that represents the sample
space.
Represent events as ovals within the rectangle.
The ovals should overlap if the events have
outcomes in common.
Example

Toss two coins.
Event A = exactly one coin is heads.
 Event B = the first coin is heads.

S
A
B
HT
HH
TH
TT
Let’s Do It!


Let’s do it! 7.7, p. 390 – Expressing Events.
Let’s do it! 7.8, p. 391 – Favor or Oppose.