* Identify events as independent or dependent * Calculate the probabilities of independent and dependent events

1. Independent & Dependent Events
The student is able to (I can):
• Identify events as either independent or dependent
• Calculate the probabilities of independent and dependent
events

2. To find the probability of two or more events occuring,
multiply the probabilities of the individual events.
independent events – events in which the outcome of each
event does NOT affect the outcome of other events.
Key words: replace, return
dependent events – events in which the outcome of one or
more events changes based on the outcome of
another event
Key words: set aside, used, without replacement

3. Examples: Identify the events as independent or dependent
and calculate the probabilities.
If I have 10 t-shirts, 4 long-sleeve shirts, 6 tank tops, and 3
sweatshirts, what is the probability that I randomly pull out
an article without sleeves, replace it, and then pull out an
article with sleeves?

4. Examples: Identify the events as independent or dependent
and calculate the probabilities.
If I have 10 t-shirts, 4 long-sleeve shirts, 6 tank tops, and 3
sweatshirts, what is the probability that I randomly pull out
an article without sleeves, replace it, and then pull out an
article with sleeves?
Since I am pulling something out and replacing it, this is an
independent event. There are a total of 10+4+6+3=23
possible items. 10+4+3=17 of them have sleeves. The
probability is therefore
 = 
6 17 102
0.193 or 19.3%
23 23 529

5. Examples: Identify the events as independent or dependent
and calculate the probabilities.
I have 50 socks in a drawer, 12 blue, 10 green, 12 red, and 16
white. What is the probability that I randomly pull out both
white socks?

6. Examples: Identify the events as independent or dependent
and calculate the probabilities.
I have 50 socks in a drawer, 12 blue, 10 green, 12 red, and 16
white. What is the probability that I randomly pull out both
white socks?
Since I am pulling one sock, not replacing it, and pulling out
another, this is a dependent event. For the second
probability, not only do the total number of socks decrease,
but the number of white socks decrease as well:
16 15 240 24
0.098 or 9.8%
50 49 2450 245
 = = 

7. Examples: Identify the events as independent or dependent
and calculate the probabilities.
If I flip a coin 3 times, what is the probability that I will get
heads, then tails, then heads again?

8. Examples: Identify the events as independent or dependent
and calculate the probabilities.
If I flip a coin 3 times, what is the probability that I will get
heads, then tails, then heads again?
Flipping a coin will always be an independent event. It
doesn’t matter if you’ve gotten heads 10 times in a row, the
probability that you will get heads or tails is always 50%.
The probability in this case is
1 1 1 1
0.125 or 12.5%
2 2 2 8
  = =

9. Examples: Identify the events as independent or dependent
and calculate the probabilities.
I have a bag of fruit containing 3 apples, 3 oranges, and 5
bananas. If I randomly pull out 4 fruits and eat them, what is
the probability that I will pull out a banana, then an orange,
then another banana, and finally, an apple?

10. Examples: Identify the events as independent or dependent
and calculate the probabilities.
I have a bag of fruit containing 3 apples, 3 oranges, and 5
bananas. If I randomly pull out 4 fruits and eat them, what is
the probability that I will pull out a banana, then an orange,
then another banana, and finally, an apple?
Since there is no replacement, this is a dependent event.
There are a total of 3+3+5+4=11 fruits. The probability of
this sequence is
5 3 4 3 180 1
0.023 or 2.3%
11 10 9 8 7920 44
   = = 