Download Independent Event

Independent and
Dependent Events
Goal:
To find the probability of two
independent or two dependent
events.
Independent Events

Events for which the occurrence of the FIRST
DOES NOT effect that of the SECOND because:
1. The
two events are unrelated
OR
2. You
repeat an event with an item whose numbers
will not change (ex: spinners or dice)
OR
3. You
repeat the same activity, but you REPLACE
the item that was removed.
Independent Events #1
The two events are unrelated
P(choosing a jack, rolling a 2)
 P (spinning a 3, pulling an ace)
 P (rolling a 6, spinning a red)

Independent Events #2
You repeat an event with an item whose
numbers will not change (e.g.:
spinners, dice, flipping a coin, etc.)
Independent Events #3
You repeat the same activity by
pulling something out, but you
REPLACE the item that was
removed.
Probability of Independent
Events

When you have two independent events:





Find the probability of the first event
Find the probability of the second event
Multiply the probabilities together
Reduce your answer
For independent events A and B, the probability of both
events occurring is found by multiplying the probabilities
of the events.
 P(A
and B) = P(A) • P(B)
An Independent Event
There are 10 socks in a basket: 5 blue, 3 yellow and 2 red.
What is the probability of choosing a yellow sock and a red
replaced after the first event?
sock if the sock is
is replaced
P(yellow, red)
Yellow:
x
3
50
3
10
Replace the yellow
sock.
2
=
Red:
10
1
5
Probability of Independent Events
A bag containing 4 green marbles, 6 red marbles, and 2 white marbles.
Three marbles are drawn at random with replacement. With
replacement means that after a marble is drawn, it is replaced
before the next one is drawn. Find each probability.
1.
P(green, red, white)
2.
P(green, white, white)
3.
P(all three red)
4.
P(not green, not red, not white)
Dependent Events

Events for which the occurrence of the
FIRST AFFECTS that of the SECOND

Look for the following 2 clues to
determine if an event is dependent
 You
remove something after the first event and
DO NOT REPLACE it.
 You
ask yourself the question, “What happens
second?” and your answer is “It depends...”
Probability of Dependent Events

When you have two dependent events:






Find the probability of the first event
Figure out what has changed
 Numerator and/or denominator
Figure out the probability of the second event
Multiply the 2 probabilities together
Reduce your answer
For dependent events A and B, the probability of both
events occurring is found by multiplying the probabilities
of the events.
 P(A
and B) = P(A) • P(B)
A Dependent Event
There are 10 socks in a basket: 5 blue, 3 yellow and 2 red.
What is the probability of choosing a yellow sock and a red
sock if the sock is NOT replaced after the first event?
P(yellow, red)
Yellow:
90
1
=
10
DO NOT replace the
yellow sock.
Notice that the
x
6
3
15
Red:
2
9
denominator
changed
Probability of Dependent Events
At a meeting there are 6 juniors and 12 seniors. Four people are
selected at random, one at a time for a committee. Find each
probability.
1.
P(all juniors)
2.
P(junior, junior, senior, senior)
3.
P(senior, senior, senior, junior)
4.
P(all senior)
TEST YOURSELF
Are these dependent or
independent events?
Are these dependent or independent
events?

Tossing two dice and getting a 6 on both
of them.
Independent Event
Are these dependent or independent
events?

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.
Dependent Event
Are these dependent or independent
events?

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.
Independent Event
Are these dependent or independent
events?

You pick the letter W from a bag containing all
the letters of the alphabet. You put the W back
in the bag and pick a second time.
Independent Event
Are these dependent or independent
events?
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.
Dependent Event
Find the probability

P(jack, green)
1
5
2
x
8
2
=
40
1
20
Find the probability

P(6, not 5)
1
6
5
x
6
5
=
36
Find the probability
P(Q, Q)
1
0
 All the letters of the
alphabet are in the 26 x 25
bag 1 time
 Do not replace the
letter

0
=
650
0
Find the probability
The num. changed to a 4
because you pulled out a
striped marble. Now the bag
is missing one.
P(striped, striped)
5
 There are 10
marbles in the
x
10
bag:




4
9
20
=
90
5 striped
The denominator
5 solid changed to a 9
because we have
one less
Do not put
themarble in
the bag since we
first marble
back.
did not put it back!
2
9