10-5 Independent and
Dependent Events
Algebra 2
Slide 1
Independent Events
Whatever happens in one event has absolutely nothing
to do with what will happen next because:
1. The two events are unrelated
OR
2. You repeat an event with an item whose
numbers will not change (eg.: spinners or
dice)
OR
3. You repeat the same activity, but you
REPLACE the item that was removed.
The probability of two independent events, A and B, is equal
to the probability of event A times the probability of event B.
P(A and B) = P(A)  P(B)
Slide 2
Independent Events
Example: Suppose you spin each of these two spinners. What
is the probability of spinning an even number and a vowel?
1
P(even) =
(3 evens out of 6 outcomes)
2
1
(1 vowel out of 5 outcomes)
P(vowel) =
5
1 1 1
P(even and vowel) =  
2 5 10
1
6
P
S
5
2
O
T
3
4
R
Slide 3
Dependent Event
• What happens the during the second event
depends upon what happened before.
• In other words, the result of the second
event will change because of what
happened first.
The probability of two dependent events, A and B, is equal to the
probability of event A times the probability of event B. However,
the probability of event B now depends on event A.
P(A and B) = P(A)  P(B) dependent on A
Slide 4
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………………………………………………
3 5
15
or
P(black and black) = 
7 13
91
Slide 5
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.
Slide 6
Independent Events
Find the probability
P(jack and factor of 12) 1
5
5
x
8
5
=
40
1
8
Slide 7
Independent Events
Find the probability
• P(6 and not 5)
1
6
5
x
6
5
=
36
Slide 8
Dependent Events
Find the probability
• P(Q and 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
Slide 9