Download 10.8 – Probability of Independent and Dependent

Chapter 10 – Data
Analysis and Probability
10.8 – Probability of Independent and
Dependent Events
10.8 – Probability of Independent and
Dependent Events
 Independent Events – two events where the
outcome of one event does not affect the
outcome of the other event

Pulling a marble out of a bag, putting it back,
and pulling another
 Dependent Events – two events where the
outcome of the first event does affect the
outcome of the second event

Pulling a marble out of a bag, keeping it, then
pulling another
10.8 – Probability of Independent and
Dependent Events
 Example 1
 Tell whether the events are independent or dependent.
 Your teacher chooses students at random to put math
problems on the board. She chooses you first, and
then chooses Sam from the remaining students.

You roll a die, it shows 4. You roll the die again and it
shows 3.

There are 10 winning tickets in a collection of 500
tickets. You select a ticket, put it aside, and select
another ticket.
10.8 – Probability of Independent and
Dependent Events
 Conditional Probability – For two
dependent events A and B, the probability
that B will occur given that A has occurred

Written P(B/A)
10.8 – Probability of Independent and
Dependent Events
 Example 2
 Use the table showing the numbers of members in the
House of Representatives and Senate in the 110th US
Congress in 2007.
Democrat Republican Independent Other
House
233
201
0
0
Senate
49
49
1
1
10.8 – Probability of Independent and
Dependent Events
Democrat Republican Independent Other
House
Senate
233
49
201
49
0
1
0
1
 What is the probability that a Congress member was a
democrat?
 What is the probability that a Senate member was a
Republican?
 What is the probability that a Democrat was a member of the
House?
10.8 – Probability of Independent and
Dependent Events
 Probability of Independent and Dependent
Events

Independent Events – If A and B are
independent events, then the probability that
both A and B occur is P(A and B) = P(A) · P(B)

Dependent Events - If A and B are
dependent events, then the probability that
both A and B occur is P(A and B) =
P(A) · P(B/A)
10.8 – Probability of Independent and
Dependent Events
 Example 3

You randomly select 2 cards from a standard
deck of 52 cards. What is the probability that
the first card is a heart and the second if a
club if:

You replace the first card before selecting the
second?

You do not replace the first card?
10.8 – Probability of Independent and
Dependent Events
 Example 4
 Find the probability of drawing the given cards
at random from a standard 52-card deck with
replacement

A club, then a spade

An ace, then a queen

A face card, then a 4

A jack, then another jack
10.8 – Probability of Independent and
Dependent Events
 Example 5
 Find the probability of drawing the given cards
at random from a standard 52-card deck
without replacement

A club, then a spade

An ace, then a queen

A face card, then a 4

A jack, then another jack
10.8 – Probability of Independent and
Dependent Events
 Three or more events

You can expand the formulas for the
probabilities of two independent or dependent
events to find the probabilities of three or more
independent or dependent events
10.8 – Probability of Independent and
Dependent Events
 Example 4

Suppose your area has 8 different Internet
Service Providers (ISPs) and you and 3
friends randomly select your own ISP. What is
the probability that you all choose different
ISPs?
10.8 – Probability of Independent and
Dependent Events
HOMEWORK
10.8 Practice A Worksheet