1. Lecture 22 Section 7.1 – 7.4.1 Wed, Oct 20, 2004
Probability
Lecture 22
Section 7.1 – 7.4.1
Wed, Oct 20, 2004

2. 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.

3. 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.

4. Example: Toss 2 Coins Toss two coins and observe how each coin lands.
Draw a tree diagram:

5. Example: Toss 2 Coins Toss two coins and observe how each coin lands.
Draw a tree diagram:
1st coin H T

6. 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

7. Example: Toss 2 Coins Toss two coins and observe how each coin lands.
Draw a tree diagram:
2nd coin
1st coin H H T H T T

8. Example: Toss 2 Coins Toss two coins and observe how each coin lands.
Draw a tree diagram:
Sample
Space
2nd coin
1st coin H HH H T HT H TH T T TT

9. Example: Toss 2 Coins
The sample space is the set
{HH, HT, TH, TT}.

10. 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.

11. 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.

12. 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

13. 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.