Chapter 9 Section 7
Chapter 12 Section 2
Algebra 2 Notes
February 12, 2009
Warm-Ups

What is the probability that you will roll exactly
five sixes in ten tosses of a standard die?

6% of the circuit boards assembled at a certain
production plant are defective. If five circuit
boards are chosen at random, what is the
probability that exactly two are defective?
Probability of Multiple Events
SECTION 9.7
Multiple Events

Dependent Event: When the outcome
of one event affects the outcome of a
second event

Examples:
◦ Pick a flower from a garden. Then pick another flower
from the same garden.
◦ Select a marble from a bag of multicolored marbles.
Put that marble aside ad select a second marble from
the same bag.
Multiple Events

Independent Events: When the
outcome of one event does not affect the
outcome of a second event.

Examples:
◦ Rolling a standard die and then flipping a coin
◦ Spin a spinner, then select a marble from a bag of
multicolored marbles.
◦ Select a marble from a bag of marbles. Replace the
marble and then select again
Independent Events

Suppose that A and B are independent
events. Then:
Independent Events

Example 1: A box contains 20 red marbles
and 30 blue marbles. A second box contains 10
white marbles and 47 black marbles. If you
choose one marble from each box without
looking, what is the probability that you get one
blue marble and one black marble?
Independent Events

Example 2: Suppose your favorite radio station is
running a promotional campaign. Every hour, four callers
chosen at random get to compete to win $100!! You call
the radio station once after 7:00am and again after
3:00pm. What is the probability that you will be one of
the four callers both times you call?
HOUR
CALLS RECEIVED
THAT HOUR
7:00 A.M.
125
3:00 P.M.
200
Mutually Exclusive Events

Mutually Exclusive Events: Two events that
cannot happen at the same time
◦ If A and B are mutually exclusive events, then
P(A and B) = 0

Determine if each event is mutually exclusive:
◦ Rolling a 2 or a 3 on a standard die
◦ Rolling an even number or a multiple of 3 on a
standard die
Probability of (A or B)

If A and B are mutually exclusive events:

If A and B are not mutually exclusive events
Probability of (A or B)

Example 1: About 53% of U.S. college students are
under 25 years old. About 21% of U.S. college students
are over 34 years old. What is the probability that a
college student chosen at random is under 25 or over
34?

Example 2: Suppose you reach into a bowl of 3 red
apples, 3 green apples, 1 lime, 1 lemon, and 2 oranges.
What is the probability that the fruit is an apple or
green?
Quick Note

When the problem asks you to find the
probability of event A and event B, you
will multiply the two probabilities

When the problem asks you to find the
probability of event A or event B, you will
add the two probabilities
Conditional Probability
SECTION 12.2
Finding Conditional Probability

Conditional Probability: contains a
condition that may limit the sample space
for an event.
◦ Write as
which stands for “the
probability of event B, given event A.”
Finding Conditional Probability

The following table shows the results of a
class survey. Find the conditional
probability:
Did you do a chore last night?
MALE
YES
7
NO
8
FEMALE
7
6
Conditional Probability Formula

Researchers asked shampoo users whether they apply
shampoo directly to the head or indirectly using a hand.
Find the probability that a respondent applies shampoo
directly to the head, given the respondent is female.
Applying Shampoo
MALE
FEMALE
Directly to
Head
2
Into Hand
First
18
6
24
Conditional Probability Formula

Eighty percent of airline flights depart on
schedule. Seventy-two percent of its flights
depart and arrive on schedule. Find the
probability that a flight that departs on time
also arrives on time.
Making a Tree Diagram

A student in Buffalo, New York, made the
observations below:
◦ Of all snowfalls, 5% are heavy (at least 6 in.)
◦ After a heavy snowfall, schools are closed 6% of the
time
◦ After a light snowfall (less than 6 in.) schools are
closed 3% of the time.
Find the probability that the snowfall is light
and the schools are open.
Homework #23
 Pg
534 #1, 2, 5, 6, 9-11, 14, 15,
18, 19, 24, 25, 36-38
 Pg
656 #1-9, 11, 12, 20, 21