9.7 Probability of Multiple Events
12.2 Conditional Probability
Small opportunities are often the beginning of
great enterprises.
Compound Events
Compound Events
Independent Events
(One event does
not affect another
event)
Dependent Events
(One event affects
another event)
Compound Events
Probability of Independent Events:
P A and B   P A  P B 
1
2
3
3
Ex1) What is the probability of spinning a 3 on the spinner and
rolling a 3 on the die?
Compound Events
Ex2) 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
Ex3) 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.
Compound Events
Mutually Exclusive Events: two events that CANNOT
happen at the same time.
Probability with “OR”:
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 
Ex4) Practice Problems
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) =
Conditional Probability
Conditional Probability Formula:
For any two events A and B from a sample space with P A  0 ,
P A and B 
P  B | A 
P  A
“given”
The table shows the results of a class survey.
Ex5) Find P(own a pet | female)
Conditional Probability
Ex6) 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)
Conditional Probability
Fudge Sauce
No Fudge Sauce
Total
Vanilla Ice Cream
64
68
132
Chocolate Ice Cream
41
27
68
Total
105
95
200
c. P(chocolate ice cream | includes fudge sauce)
d. P(vanilla ice cream with no fudge sauce)
e. P(vanilla ice cream | does not include 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
e. Find the probability that the order has no fudge sauce, given that it
has vanilla ice cream.
f. P(vanilla ice cream)
Tree Diagrams
Ex 7) A student made the following observations
of the weather in his hometown.
• On 28% of the days, the
sky was mostly clear.
• During the mostly clear days, it
rained 4% of the time.
• During the cloudy days it
rained 31% of the time.
a. Use a tree diagram to find the probability that a day will start out
clear, and then it will rain.
b. Find the probability that it will not rain on any given day.
9.7 Probability of Multiple Events
12.2 Conditional Probability
HW: pg. 534 #1-7 odd, 11-25 odd, 31-39 odd
pg. 656 #1-13 all
Small opportunities are often the beginning of
great enterprises.