Download Notes for Lesson 10-7: Independent and Dependent Events

Notes for Lesson 10-7: Independent and Dependent Events
10-7.1 – Classifying Events as Independent or Dependent
Vocabulary:
Independent Events – Events for which the occurrence or non-occurrence of one event does not affect
the probability of the other event
Dependent Events – Events for which the occurrence or non-occurrence of one event affects the
probability of the other 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.
Example: Adam’s teacher gives the class two lists of titles and asks each student to choose two of them. Adam
can change two titles one from each list or both from the same list. If Adam chooses one title from each list
then the events would be Independent of each other because the first book he chooses does not affect the
choices of the second. If he chooses two books from the same list then the probability of the second choice
changes because he has taken one book out of the list and therefore changes the number of outcomes.
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
10-7.2 – 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?
10 10 100
1 1 1 1 1
A coin is flipped 4 times. What is the probability it will land on heads all four times? * * * 
2 2 2 2 16
10-7.3 – 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
Do Practice B #’s 1 – 10 even