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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
Joann flips a coin and gets a head. Then she rolls a 6 on a number cube.
independent.
Decide whether the set of events are dependent or independent.
1
Kathy draws a 4 from a set of cards numbered 1–10 and rolls a 2 on a number cube.
independent.
Sam chooses a book from the shelf to read, and then Janette chooses a book from the books that remain.
dependent.
2
3
4 John draws a card numbered 1–10 and replaces it and draws another card.
John draws a card numbered 1–10 and does not replaces it and draws another card.
5
dependent.
independent.
To find the probability that two independent events will happen, multiply the probabilities of the two events.
Probability of Two Independent Events
= X
Probability of both events
Probability offirst event
Probability of second event
P(A and B) P(A) P(B)
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)16
14
16
124X
14
36
324X =
18=
34
36
924X =
38=
24
26
424X = =
Thomas roles a number cube 3 times. Find the probability of the following.
P(3) = 1/6 = 1/216
P(even) = 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 =16
1/61/6
1/2 1/2
X X
X X
X X X2 2 2
P(Yellow then Blue) =
P (Pink then not blue) =
P(Yellow then Yellow) =
332= =
=
28
38
14
38
28
28
14
14
08
58
064
•
•
••
•
116=
=
With Replacing
0=
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
= •
Probability of both events
Probability offirst event
Probability of second event after A occurs
P(A and B) P(A) P(B following A)
P(Yellow then Blue) =
P (Purple then Purple) =
P(Yellow then Yellow) =
328= =
=
28
37
14
37
28
17
14
17
18
07
056
•
•
••
•
128=
=
With Out Replacing
0=
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 2Orange Shades 4
Yellow Shades 1
Green Shades 2
Blue Shades 4Purple Shades 3
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?
A blue shade and then a orange shade?
A yellow shade and then a yellow shade?
216
315
•
416
415
•
116
015
•
18
15
•
14
415
•
= = 140
=
= 0
=1
1 115
AssignmentPage 423 – 424Problems 1-9
Page 423 – 424Problems 1-9, 10
Independent and Dependent Probability
Date _____________
Insert Lesson Title Here
Joann flips a coin and gets a head. Then she rolls a 6 on a number cube.
Decide whether the set of events are dependent or independent.
1
Kathy draws a 4 from a set of cards numbered 1–10 and rolls a 2 on a number cube.
Sam chooses a book from the shelf to read, and then Janette chooses a book from the books that remain.
2
3
4 John draws a card numbered 1–10 and replaces it and draws another card.
John draws a card numbered 1–10 and does not replaces it and draws another card.
5
To find the probability that two independent events will happen, multiply the probabilities of the two events.
Probability of Two Independent Events
= X
Probability of both events
Probability offirst event
Probability of second event
P(A and B) P(A) P(B)
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
= •
Probability of both events
Probability offirst event
Probability of second event after A occurs
P(A and B) P(A) P(B following A)
y b
g p
br
b y
P(Yellow then Blue) =
P (Purple then Purple) =
P(Yellow then Yellow) =
With Out Replacing
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 shadesOrange Shades
Yellow Shades
Green Shades
Blue ShadesPurple Shades
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?
A blue shade and then a orange shade?
A yellow shade and then a yellow shade?
