Download Independent Probability

Independent and Dependent
Probability
Independent events - the occurrence of one event
has no effect on the probability that a second event
will occur.
Dependent events, the occurrence of one event does
have an effect on the probability that a second event
will occur.
Insert
Lesson
Title
Here
Decide whether the set of events are dependent or
independent.
1
Joann flips a coin and gets a head. Then she
rolls a 6 on a number cube.
independent.
2 Sam chooses a book from the shelf to read, and then Janette chooses a
book from the books that remain.
dependent.
3
4
Kathy draws a 4 from a set of cards numbered 1–10 and rolls a 2 on a number
cube.
independent.
John draws a card numbered 1–10 and replaces it and draws another card.
independent.
5
John draws a card numbered 1–10 and does not replaces it and draws
another card.
dependent.
To find the probability that two independent events
will happen, multiply the probabilities of the two
events.
Probability of Two Independent Events
P(A and B)
Probability of
both events
=
P(A)
Probability of
first event
X
P(B)
Probability of
second event
An experiment consists of spinning this spinner
and rolling a number cube. Find the probability.
P(red , 4) =
1
4
X
1
6
1
= 24
P(yellow, even number)
1
4
X
3
6
1
3
= 24 = 8
P(not green, odd number)
3
3
9
3
= 8
=
X
6
24
4
P(Red or Green, 3 or 2)
1
2
4
2
= 24 = 6
4 X 6
Thomas roles a number cube 3 times. Find the probability of the
following.
P(3) = 1/6 X 1/6 X 1/6 = 1/216
P(even) = 1/2 X 1/2
X
1/2 = 1/8
Sharon has 4 coins. If Sharon flips all the coins at once, how many
outcomes are in the sample space
2
X
2
X
2
X
2
=16
With
Replacing
P(Yellow then Blue) =
2 • 3 = 1 • 3 = 3
8 8
4 8 32
P(Yellow then Yellow) =
P (Pink then not blue) =
2 • 2 =1 • 1 = 1
16
8 8
4 4
0 • 5 = 0 =
0
8
8
64
To find the probability that two dependent events
will happen, multiply the probability of A and the
probability of B after A occurs.
Probability of Two Independent Events
P(A and B)
Probability of
both events
=
P(A) • P(B following A)
Probability of
first event
Probability of
second event
after A occurs
With Out
Replacing
P(Yellow then Blue) =
2 • 3 = 1 • 3 = 3
8 7
4 7 28
P(Yellow then Yellow) =
P (Purple then Purple) =
2 • 1 =1 • 1 = 1
28
8 7
4 7
1 • 0 = 0 =
0
7
8
56
Mary is getting ready to paint her bedroom. Her
mother went to the store and purchased samples for
her to choose from.
Colors
# of samples
Red shades
Orange Shades
2
4
Yellow Shades
1
If she randomly picks a color
sample then does not replace it
and picks another color sample,
then what is the probability of
Mary choosing ……
A red shade and then a purple shade?
2
2 • 3
1 • 1 = 1
=
40
15
5
16
8
A blue shade and then a orange shade?
Blue Shades
4
4 • 4 =
1 • 41 = 1
15
15
15
16
1 4
A yellow shade and then a yellow shade?
Purple Shades
3
Green Shades
1 • 0
15 = 0
16
Assignment
Page 423 – 424
Problems 1-9
Page 423 – 424
Problems 1-9, 10
Date _____________
Independent and Dependent
Probability
Insert
Lesson
Title
Here
Decide whether the set of events are dependent or
independent.
1
Joann flips a coin and gets a head. Then she
rolls a 6 on a number cube.
2 Sam chooses a book from the shelf to read, and then Janette chooses a
book from the books that remain.
3
Kathy draws a 4 from a set of cards numbered 1–10 and rolls a 2 on a number
cube.
4
John draws a card numbered 1–10 and replaces it and draws another card.
5
John draws a card numbered 1–10 and does not replaces it and draws
another card.
To find the probability that two independent events
will happen, multiply the probabilities of the two
events.
Probability of Two Independent Events
P(A and B)
Probability of
both events
=
P(A)
Probability of
first event
X
P(B)
Probability of
second event
An experiment consists of spinning this spinner and rolling a
number cube. Find the probability.
P(red , 4)
P(yellow, even number)
P(not green, odd number)
P(red or green, 3 or 2)
Thomas roles a number cube 3 times. Find the probability of the
following.
P(__)
P(______)
Sharon has ___ coins. If Sharon flips all the coins at once, how
many outcomes are in the sample space
To find the probability that two dependent events
will happen, multiply the probability of A and the
probability of B after A occurs.
Probability of Two Independent Events
P(A and B)
Probability of
both events
=
P(A) • P(B following A)
Probability of
first event
Probability of
second event
after A occurs
With Out
Replacing
y
r
b
b
g
b
y
p
P(Yellow then Blue) =
P(Yellow then Yellow) =
P (Purple then Purple) =
Mary is getting ready to paint her bedroom. Her
mother went to the store and purchased samples for
her to choose from.
Colors
Red shades
Orange Shades
# of samples
If she randomly picks a color
sample then does not replace it
and picks another color sample,
then what is the probability of
Mary choosing ……
Yellow Shades
A red shade and then a purple shade?
Green Shades
A blue shade and then a orange shade?
Blue Shades
Purple Shades
A yellow shade and then a yellow shade?