Download Lesson 12-8

Notes for Lesson 12 – 8: Independent and Dependent Events
12-8.1 – Mutually Exclusive or Overlapping events
Sometimes you want to know the probability when 2 or more things can happen. Such as when you roll the
1+1
2
1
dice and a 4 or a 5 would be a good result. So that probability would be 𝑃(4 𝑜𝑟 5) = 6 = 6 𝑜𝑟 3. Or if you
are playing cards and a diamond or 4 would be a good card the probability would be 𝑃(𝑑𝑖𝑎𝑚𝑜𝑛𝑑 𝑜𝑟 4) =
13+3
16
4
= 52 𝑜𝑟 13 because there are 13 diamonds in a deck plus 3 more 4’s that aren’t already diamonds.
52
12-8.2 – Classifying Events as Independent or Dependent
Vocabulary:
Compound Events – An event that consists of two or more events
Independent Events – When the outcome of one event does not affect the probability of a second event
Dependent Events – When the outcome of one event affects the probability of a second event
When one outcome depends on outcome of another event, or when one event affects the probability of the other
then the two events are connected to each other and are said to be Dependent Events. If two event that happen
at the same time do not affect the probability of each other then the two events are Independent of each other.
A dime lands heads up and a nickel lands heads up – Independent
You choose a game piece and then your friend chooses a game piece – Dependent
One student is chosen for a project and then another student is chosen for a second project – Dependent
A number cube lands on a 2 and then is rolled again and lands on a 6 – Independent
12-8.3 – Finding the probability of Independent or Dependent events
To find the probability of finding the probability of two events happening together is the product of the
probability of each event separately. P(A and B)=P(A)*P(B)
So, the probability of rolling double 4’s on a pair of dice would be
1 1 1
* 
6 6 36
Examples:
What is the probability of being dealt a black jack? P(Ace) = 1/13 * P(Value of Ten) = 16/51 so
1 16 16
* 
13 51 663
In a jar there are 7 blue marbles and 3 yellow marbles. What is the probability of drawing a yellow and then a
3 7
21
* 
blue marble if the first marble is replaced?
(Independent)
10 10 100
3
7
21
7
If the first marble is not replaced? 10 ∗ 9 = 90 𝑜𝑟 30 (Dependent)
A coin is flipped 4 times. What is the probability it will land on heads all four times?
1 1 1 1 1
* * * 
2 2 2 2 16
12-8.4 – Problem-Solving Applications
There are 7 pink flowers and 5 yellow flowers in a bunch. Jane selects a flower at random and then Leah
selects a flower at random from the remaining flowers.
7 5
35
* 
12 11 132
What is they select 2 pink flowers?
7 6
42
7
∗
=
𝑜𝑟
12 11 132
22