1. 1.6 Probability9.7 Probability of Multiple Events
12.2 Conditional Probability

2. Measures how likely it is that an event will occur.
Probability
Measures how likely it is that an event will occur.
Expressed as
A Percentage (0-100%) or
a number between 0 and 1

3. Lesson Notes 9.7 and 12.2 Probability Examples
Experimental Probability
Lesson Notes 9.7 and 12.2 Probability Examples
Experimental Probability: Based on observation
Ex1)
A quarterback throws 40 passes during a game and completes 30 of them. Find the experimental probability of him completing a pass.

4. Lesson Notes 9.7 and 12.2 Probability Examples
Theoretical Probability
Lesson Notes 9.7 and 12.2 Probability Examples
(Theoretical) Probability: Based on what would happen in theory.
Ex2)
Find the probability of rolling a prime number when you roll a regular six-sided die.

5. Example from Venn diagram
Ex 3) What is the probability of drawing a heart that is not a face card from a deck of 52 cards.
Everything else
Hearts
Face Cards

6. Lesson Notes 9.7 and 12.2 Probability Examples
9.7 Probability of Multiple Events
Lesson Notes 9.7 and 12.2 Probability Examples
Compound Events
Independent Events (One event does not affect another event)
Dependent Events (One event affects another event) 6

7. Lesson Notes 9.7 and 12.2 Probability Examples
Probability that both Independent Events will occur: 1 2 3
Ex 4) What is the probability of spinning a 3 on the spinner and rolling a 3 on the die? 7

8. Lesson Notes 9.7 and 12.2 Probability Examples
Compound Events
Ex 5) A card is drawn from a standard 52-card deck. Then a die is rolled. Find the probability of each compound event.
P(draw heart and roll 6)
P(draw 7 and roll even
P ( draw face card and roll < 6) 8

9. Lesson Notes 9.7 and 12.2 Probability Examples
Compound Events
Lesson Notes 9.7 and 12.2 Probability Examples
Ex 6) There are five discs in a CD player. The player has a “random” button that selects songs at random and does not repeat until all songs are played. What is the probability that the first song is selected from disc 3 and the second song is selected from disc 5?
Disc songs
Disc songs
Disc songs
Disc songs
Disc songs 9

10. Lesson Notes 9.7 and 12.2 Probability Examples
Why are these independent events?
Ex 7) A drawer contains 4 green socks and 5 blue socks. One sock is drawn at random. Then another sock is drawn at random.
a. Suppose the first sock is returned to the drawer before the second is drawn at random. Find the probability that both are blue.
b. Suppose the first sock is not returned to the drawer before the second is drawn. Find the probability that both are blue. 10

11. Lesson Notes 9.7 and 12.2 Probability Examples
Probability with “OR”
What is the probability event A or event B could occur?
Mutually Exclusive Events: two events that CANNOT happen at the same time
If A and B are mutually exclusive events, then
If A and B are not mutually exclusive events, then
Subtract the overlap 11

12. Lesson Notes 9.7 and 12.2 Probability ExamplesOR
Lesson Notes 9.7 and 12.2 Probability Examples
Example 8)
P(face card) =
P(non-face card) =
P(face card or ace) =
P(two or card < 6) =
P(not a jack) =
P(red card or seven) =
P(ace or king) = 12

13. HW Assignment
Section 6.7 “Basic” Probability p. 42 #6-14 (even), Section 9.7 “multiple event” Probability p. 534 #1,2, 5, 9, 13, 16, (odd),37,39,45 p. 542 #36 Section 12.2 “Conditional” Probability p. 136 #1-13 all

14. Lesson Notes 9.7 and 12.2 Probability Examples
Yes, Did a chore last night
No, Did NOT do a chore
Male 2 7
Female 6 3 14

15. Lesson Notes 9.7 and 12.2 Probability Examples
Section 12.2: Conditional Probability
Lesson Notes 9.7 and 12.2 Probability Examples
Conditional Probability Formula:
“Probability of event B, given that event A has occurred”
“given”
Yes, Did a chore last night
No, Did NOT do a chore
Male 2 7
Female 6 3
Ex 10) 15

16. Lesson Notes 9.7 and 12.2 Probability Examples
Conditional Probability
Ex 11) A cafeteria offers vanilla and chocolate ice cream, with or without fudge sauce. The manager kept records on the last 200 customers who ordered ice cream.
Fudge Sauce
No Fudge Sauce
Total
Vanilla Ice Cream 64 68
132
Chocolate Ice Cream 41 27
105 95
200
a. P(includes fudge sauce)
b. P(includes fudge sauce | chocolate ice cream)
c. P(chocolate ice cream | includes fudge sauce) 16

17. Lesson Notes 9.7 and 12.2 Probability Examples
Conditional Probability
Fudge Sauce
No Fudge Sauce
Total
Vanilla Ice Cream 64 68
132
Chocolate Ice Cream 41 27
105 95
200
d. P(vanilla ice cream with no fudge sauce)
e. P(vanilla ice cream | does not include fudge sauce)
f. Find the probability that the order has no fudge sauce, given that it has vanilla ice cream. 17

18. Tree Diagrams – Ex 12)