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)
You repeat the same activity, but you REPLACE the item that was removed.

3. The two events are unrelated
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 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 3 10 2 10 1 5 3 50 P(yellow, red) Yellow:
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. Notice that the denominator changed
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. Are these dependent or independent events?
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 25 650 P(Q, Q)25
650 x =
P(Q, Q)
All the letters of the alphabet are in the bag 1 time
Do not replace the letter

22. Find the probability P(striped, striped)
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