1.6
Probability
9.7
Probability
of Multiple
Events
12.2
Conditional
Probability
Probability
Measures how likely it is that an event will occur.
Expressed as
A Percentage (0-100%)
or
a number between 0 and 1
Experimental Probability
Experimental Probability: Based on observation
number of times the favorable event occurs
P
number of trials in experiment
Ex1)
A quarterback throws 40 passes during a game and completes 30 of
them. Find the experimental probability of him completing a pass.
# of complete passes
P
# of total passes
30
3

 or 75%
4
40
Theoretical Probability
(Theoretical) Probability: Based on what would happen
in theory.
number of favorable events
P
number of possible outcomes
Ex2)
Find the probability of rolling a prime number when you roll a
regular six-sided die.
# of prime numbers
P
# of possibilities

3
1
 or 50%
2
6
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
9.7 Probability of Multiple Events
Compound Events
Independent Events
(One event does
not affect another
event)
Dependent Events
(One event affects
another event)
AND
Probability that both Independent Events will occur:
P A and B   P A  PB 
1
2
3
3
Ex 4) What is the probability of spinning a 3 on the spinner and
rolling a 3 on the die?
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.
a) P(draw heart and roll 6)
b) P(draw 7 and roll even
c) P ( draw face card and roll < 6)
Compound Events
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 1
8 songs
Disc 2
10 songs
Disc 3
13 songs
Disc 5
10 songs
Disc 4
9 songs
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.
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
P A or B   P A  P B 
If A and B are not mutually exclusive events, then
P A or B   P A  P B   P A and B 
Subtract the overlap
OR
Example 8)
a. P(face card) =
b. P(non-face card) =
c. P(face card or ace) =
d. P(two or card < 6) =
e. P(not a jack) =
f. P(red card or seven) =
g. P(ace or king) =
HW Assignment
Section 6.7 “Basic” Probability
p. 42 #6-14 (even), 25-33
Section 9.7 “multiple event” Probability
p. 534 #1,2, 5, 9, 13, 16, 19-25 (odd),37,39,45
p. 542 #36
Section 12.2 “Conditional” Probability
p. 136 #1-13 all
Example 9)
Yes, Did a chore
last night
No, Did NOT do
a chore
Male
2
7
Female
6
3
Pfemale  
Pdid a chore last night  
Pfemale AND did a chore last night  
Section 12.2: Conditional Probability
Conditional Probability Formula:
“Probability of event B, given that event A has occurred”
P A and B 

P  A
P B | A
“given”
Ex 10)
Yes, Did a chore
last night
No, Did NOT do
a chore
Male
2
7
Female
6
3
Pfemale | did a chore last night  
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
68
Total
105
95
200
a. P(includes fudge sauce)
b. P(includes fudge sauce | chocolate ice cream)
c. P(chocolate ice cream | includes fudge sauce)
Conditional Probability
Fudge Sauce
No Fudge Sauce
Total
Vanilla Ice Cream
64
68
132
Chocolate Ice Cream
41
27
68
Total
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.
Tree Diagrams – Ex 12)