Download Dependent Events

9.7 Dependent and Independent
Events
Mr. Swaner
Notes
Independent events are not influenced by any
other event. That is, the event does not depend on
what happens elsewhere.
Ex. If I am picking out a shirt from my closet and a tie out of my drawer,
the number of shirts and number of ties have no effect on the probability of
one another.
No matter what shirt I pull out of the closet, there are the same number of
ties in the drawer. The shirt selection has no effect on the tie selection.
Notes
Dependent Events are influenced by other events.The
probability of the event depends on what happens elsewhere
Ex. Let’s say I am taking shirts out of my closet again. The probability
of the shirt I pick second will depend on which shirt was pulled out first
I have 2 red shirts, a blue shirt, and a green shirt. If my first selection is a
green shirt and I don’t put it back, what is the probability that I pick a green
shirt the second time?
It is impossible! There are none left.
Let’s See if We Can Determine if the
Probability of Events are Independent
or Dependent
1. Getting heads on a coin toss and rolling a 6 on a dice.
2. Getting 3 red gumballs out of a machine of different colors
3. Pulling out two matching socks one at a time from a drawer of mixed socks.
4. A football team wins 2 games in a row.
5. Drawing the names of 2 brothers out of a hat of 10 names
Lets Try Some Independent Events
1. Getting heads on a coin toss and rolling a 6 on a dice.
What is the probability of getting heads on a coin toss?
What is the probability of rolling a 6 on a dice?
1
2
1
6
When determining the overall probability we generally multiply the two
probabilities together when the word
and is used
1 1 1
 
2 6 12
When determining the overall probability we generally add the two
probabilities when the word
or is used
More Independent Events
4. A football team wins 2 games in a row.
What is the probability of the team winning the first game?
1
2
What is the probability of the team winning the second game?
1
2
The question is really asking,” what is the probability that the team wins
the first game and the second game?”
are we going to add or multiply?
1 1 1
 
2 2 4
or 25%
Not Today
Let’s go back to the first one
 Getting heads on a coin toss and
or rolling a 6 on a dice
1 1
4 2
  
2 6
6 3
Dependent Events
 You have a bag of 10 marbles: 3 red, 4 blue, 2 green, and 1
purple.
 What is the probability of picking red first then green if you
only pick two and do not replace them?
 Probability of picking red =
3
10
 Probability of picking green =
2
9
 What is the probability of picking red first then green if you
only pick two and do not replace them?
3 2
 
10 9
Another
2. Getting 3 red gumballs in a row out of a machine of different colors
There is not enough information here to determine the probability but we know that the probability
depends on how many red gumballs there are, and how many gumballs there are total.
Let’s say there are 9 red gumballs and 18 gumballs altogether.
favorable
total
9
18
How many red are left now?
that is the odds of getting the first red gumball
8
17
How many total are left now
Now we have to get one more red. What is the probability this time?
7
16
Continued
9
18
 The odds of getting the first red are:
 The odds of getting the second red are:
 The odds of getting the third red are:
7
16
8
17
What are the odds of getting a red and a red and a red in a row?
9 8 7
 
18 17 16
504

4896
 10%
Dependent Event
Example: There are 6 black pens and 8 blue pens in a jar. If you
take a pen without looking and then take another pen without
replacing the first, what is the probability that you will get 2
black pens?
P(black first) =
6
3
or
14
7
5
P(black second) =
(There are 13 pens left and 5 are black)
13
THEREFORE………………………………………………
P(black, black) =
3 5
15

or
7 13
91
Dependent Event
Example: There are 6 black pens and 8 blue pens in a jar. If you
take a pen without looking and then take another pen without
replacing the first, what is the probability that you will get:
P(blue first) =
P(black second) =
P(blue, black) =
Dependent Event
Example: There are 6 black pens and 8 blue pens in a jar. If you
take a pen without looking and then take another pen without
replacing the first, what is the probability that you will get:
P(blue first) =
P(blue second) =
P(blue, blue) =
TEST YOURSELF
Are these dependent or independent events?
1.
Tossing two dice and getting a 6 on both of them.
2.
You have a bag of marbles: 3 blue, 5 white, and 12 red.
You choose one marble out of the bag, look at it then put it
back. Then you choose another marble.
3.
You have a basket of socks. You need to find the
probability of pulling out a black sock and its matching
black sock without putting the first sock back.
4.
You pick the letter Q from a bag containing all the letters of
the alphabet. You do not put the Q back in the bag before
you pick another tile.
Probability of Dependent Events
 A basket contains 6 apples, 5 bananas, 4 oranges, and 5
peaches. Leslie randomly chooses one piece of fruit, eats it,
then chooses another. What is the probability that she chose a
banana and then an
apple?
Dependent Events
Find the probability
 P(Q, Q)
 All the letters of the
alphabet are in the bag 1
time
 Do not replace the letter
1
26
0
x
25
0
=
650
0
Probability of Three Dependent Events
 You and two friends go to a restaurant and order a
sandwich. The menu has 10 types of sandwiches and each
of you is equally likely to order any type. What is the
probability that each of you orders a different type?
 There are 20 dogs at the dog park. 3 are brown, 9 are
black, 6 are white, and 2 are yellow. You will not replace
each dog before the next selection.
P(white, black)
 There are 20 dogs at the dog park. 3 are brown, 9 are
black, 6 are white, and 2 are yellow. You will not replace
each dog before the next selection.
P(yellow, yellow)
Closure
 When you see the word AND, that means…….?
 When you see the word OR, that means……?