Independent and Dependent Events

1
Independent and Dependent Events

• Compound Events
• Lessons 11-7 11-9

2
Independent Events

• Whatever happens in one event has absolutely
  nothing to do with what will happen next because
• The two events are unrelated
• OR
• You repeat an event with an item whose numbers
  will not change (eg. spinners or dice)
• OR
• You repeat the same activity, but you REPLACE the
  item that was removed.

3
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)

4
Independent Events 2

• You repeat an event with an item whose numbers
  will not change (e.g. spinners, dice, flipping a
  coin, etc.)

5
Independent Events 3

• You repeat the same activity by pulling something
  out, but you REPLACE the item that was removed.

6
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.

7
Dependent Event

• Look for the following 2 clues to determine if an
  event is dependent
• You repeat the same event
• 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...

8
Representing and Solving for a Compound Event

• Two events are listed and there is a comma in
  between them.
• P(yellow, yellow)
• P(heads, tails)
• P(6, even number)
• P(not 6, not 5)
• Events must occur in the order listed.
• Figure out the probability of the first event and
  multiply it by the probability of the second
  event.
• Remember that the probability of a second event
  changes in dependent events.
• It does not change with an independent event.

9
Solving 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
• Remember that the two events have nothing to do
  with one another because they involve 2 separate
  items OR one item, but things are replaced after
  the first draw.

10
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 sock if the sock is
  replaced after the first event?

is replaced
P(yellow, red) Yellow Replace the yellow
sock. Red
3
10
x
2
10
1
5

3
50
11
Solving 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
• Remember that the two events are interconnected.
• Items are NOT replaced after being pulled out.

12
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?

is NOT replaced
P(yellow, red) Yellow DO NOT replace the
yellow sock. Red
3
10
Notice that the denominator changed
x
2
9
6
90
1
15

13
TEST YOURSELF

• Are these dependent or independent events?

14
Are these dependent or independent events?

• Tossing two dice and getting a 6 on both of them.

Independent Event
15
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
16
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
17
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
18
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
19
Find the probability
1
5
2
8
2
40
x

• P(jack, green)

1
20
20
Find the probability
1
6
5
6
5
36
x

• P(6, not 5)

21
Find the probability
1
26
0
25
0
650
x

• P(Q, Q)
• All the letters of the alphabet are in the bag 1
  time
• Do not replace the letter

0
22
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)
• There are 10 marbles in the bag
• 5 striped
• 5 solid
• Do not put the first marble back.

5
10
4
9
20
90
x

The denominator changed to a 9 because we have
one less marble in the bag since we did not put
it back!
2
9