Dependent
vs.
Independent
Independent:
The probability of one event has no affect on another event occurring
*The events are independent of each other
Dependent:
One event influences the likelihood of another event occurring
*The events are dependent of each other
Question to ask:
Is it possible for the
events to occur in any order for independent and dependent events?
What are some examples of independent events?
(Events where the order does not matter)
Brushing your hair then going on a walk.
Rolling a die 50 times
Picking a card from a deck then rotating a spinner
What are some examples of dependent events?
(Events where the order DOES matter)
Speeding then getting a speeding ticket
Picking a marble out of a bag then drawing another marble WITHOUT replacing the first one
Catching 2 fish and not throwing them back in the pond
Conditional Probability:
the probability that event B occurs given
that event A has already occurred
*The conditional probability of B given A is written as P(BA)
P(BA)=P(A and B)
P(A)
Conditional Probability Formula:
Think About It!
At a high school a person wants to find the probability that a student is female or a senior if selected at random.
Think about all of the possibilities to consider before finding this probability:
1. The student is a Female.
2. The student is a Senior.
3. The student is
BOTH
a Female and a Senior
Think About It!
At a high school a person wants to find the probability that a student is senior or a freshman if selected at random.
Think about all of the possibilities to consider before finding this probability:
1. The student is a Freshman
2. the student is a Senior
What is the
DIFFERENCE
between the 2 situations when trying to find the probability???
Example 1:
*A student can be
BOTH
female and a senior
Example 2:
*A student
CANNOT
be both a senior and a freshman.
The 2nd example is called
MUTUALLY EXCLUSIVE
*Mutually Exclusive:
When 2 or more events cannot occur at the same time
What are some examples of Mutually Exclusive Events??
Being a tea cup pig or a kitten
Being in France or Australia
The time being 1 pm and 2 pm in the same time zone
FUNZIE!!
Determine if each event is mutually exclusive or not when a single card is drawn from a deck.
a. Getting a 7 and a Jack
b. Getting a Club and a King
c. Getting a Club and a Heart
d. Getting an even number and getting a 10
Probability of Mutually Exclusive Events
P(A or B)=P(A)+P(B)
EX 1:
A box of doughnuts has 5 plain, 4 jellyfilled, and 3 chocolate. If a person selects a doughnut at random what is the probability that it is a chocolate doughnut or a plain doughnut?
P(Plain or Chocolate)= P(Plain)+P(Chocolate)
P(Plain)=5/12
P(Chocolate)=3/12
P(Plain or Chocoalte)=5/12+3/12=8/12=2/3
FUNZIE!!!!
A day of the week is selected at random. Find the probability that a day on the weekend is selected.
P(Saturday or Sunday)=P(Saturday)+P(Sunday)
P(Saturday)=1/7
P(Sunday)=1/7
P(Saturday or Sunday)= 1/7+1/7=2/7
Overlapping Events:
Events that have one or more outcomes in common
(events that are NOT mutually exclusive!!)
(Can ONLY be used for nonmutually exclusive events
P(A or B)=P(A)+P(B)P(B and A)
Addition Rule
:
Practice!!
In a standard deck of 52 cards you pick out 1 card. What is the probability that the card is a club or a king?
NONMutually Exclusive Events:
P(A or B)=
P(A)
+
P(B)

P(A and B)
A: King
B: Club
P(A)=4/52
P(B)= 13/52
P(A and B)=1/52
P(A or B)=
4/52
+
13/52

1/52
=16/52=4/13
P(A or B)=4/13
Funzie!!
In a hospital there are 8 nurses and 5 doctors. 7 of the nurses and 3 of the doctors are female. If a staff member is selected at random, what is the probability that they are a male or a nurse?
P(A or B)=
P(A)
+
P(B)

P(A and B)
A:Nurses
B:Male
P(A)=8/13
P(B)= 3/13
P(A and B)=1/13
P(A or B)=
8/13
+
3/13

1/13
=10/13
P(A or B)=10/13
Which event do you think is independent, and which event do you think is dependent?
1. Picking a kitten out of a box full of kittens, petting it, and then placing it back in the box to play with later.
2. Picking a kitten out of a box full of kittens, then taking it home with you to keep :D
YES: Independent
NO: Dependent
FUNZIE!!!
Determine which events are independent and which are dependent.
1. Spinning a spinner 2 times in a row.
2. Drawing a card from a deck and not replacing it.
Ex: What is the probability of rolling a 6 on a die, and then spinning a 5 on a spinner with 5 equal sections labeled 15?
Calculating the Probability of INDEPENDENT EVENTS
P(A and B)= P(A) P(B)
EXAMPLE ANSWER
A: Rolling a 6
B: Spinning a 5
P(A and B)=P(A) P(B)
P(A)=1/6 P(B)=1/5
P(A and B)= 1/6 1/5=1/30
What is the probability of drawing a black checker from a bag filled with 6 black checkers and 4 red checkers, replacing it, and drawing another black checker?
FUNZIE!!
FUNZIE ANSWER!
A: Picking a black checker
B: Picking a black checker
P(A and B)= 6/10 6/10=3/5 3/5=9/25
Probability of Dependent Events
There are 4 black marbles and 2 white marbles in a bag. What is the probability of chosing a black marble, not replacing it, and then chosing a white marble?
FUNZIE!!!!
A: In a deck of cards, what is the probability of picking a number card and then a face card (including the ace) if you replace the cards each time? State if the events are independent or dependent.
B: What is the probability of picking 2 3's in a row if you do not replace the cards each time? State if the events are independent or dependent?
How many people in the class play a sport or are in a club?
Sport
Club
Ex: What is P(ClubSport)?
Ex: What P(Sport)
Ex: What is P(sport or club)?
FUNZIES!
Ex: What is P(SportClub)?
Ex: What P(Club)
Ex: What is P(not sport or not club)?
FUNZIE:
1) Find the probability of students are female, given that they prefer ROTC
Ex: Find the probability of students that prefer band, given that they are female.
2)Find the probability of students that prefer Ag, given that they are male
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Dependent vs. Independent Probability
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