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Sample Space - Set of all possible outcomes
for a chance experiment.
Example: Roll A Die
Example: Roll 2 DIce
UNIT 5: PROBABILITY
Basic Probability
Probability Model
• It is a description of some chance process
that consists of two parts
• A sample space (S)
Tree Diagram
A technique for listing the outcomes in a sample space. It
contains branches showing what can happen on different
trials.
Gender of 3 Children:
• A probability for each outcome
Ex: Probability Model for Rolling a Die:
Draw diagram of all possibilities of test
performance on three True/False
questions.
Draw the tree diagram for winning the best
2 out of 3 games.
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10/21/2014
Imagine rolling two fair, six-sided dice – one
that is red and one that is green. Give a
probability model for this chance process.
Event
• It is a subset of the sample space.
• It is usually designated by capital letters,
like A, B, C, and so on.
Consider flipping 2 coins
Basic Rules of Probability – (don’t write yet)
•
A = both tails
B = at least one head
Find P(A)
P(B)
Complement
Mutually Exclusive (Disjoint)
• It is the even “not” A
• Two events are mutually exclusive (disjoint)
P ( A ) = 1 − P ( A)
or
if they have no outcomes in common and
so can never occur together.
( )
P A' = 1 − P( A)
: = . =
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10/21/2014
Determine which events are mutually exclusive (disjoint) when a
single die is rolled…..
You Try…Which are mutually exclusive (or disjoint)
when a single card is drawn from a deck?......
1. Getting a 4 and a 6
1. Disjoint
1. Getting a 7 and J
1. Disjoint
2. Getting an odd #
2. Disjoint
2. Getting a club and
2. Not Disjoint
and an even #
3. Getting an odd#
and a # less than 4
4. Getting a # greater
than 4 and a # less
than 4
5. Getting a 3 and an
odd #
king
3. Getting a face card
and an ace
4. Getting a face card
and a spade
3. Not Disjoint
4. Disjoint
5.
3. Disjoint
4. Not Disjoint
Not Disjoint
Basic Probability Rules
Find the probability:
•
• Rolling a 5
• Choosing a girl in this class
• Drawing a king
A marble is pulled from a bag holding one red,
one white, one blue, and two green marbles.
A={the blue marble is drawn}
Distance learning courses are rapidly gaining popularity
among college students. Randomly select an
undergraduate student who is taking a distance-learning
course for credit, and record the student’s age. Here is
the probability model.
B={a green marble is drawn}
Age Group (Yr):
= =
= −
=
=
!
+ =
=
Probability:
−
=
=
!
18 to 23
24 to 29
30 to 39
40 or over
0.57
0.17
0.14
0.12
• Show that this is a legitimate probability model.
0 ≤ P(x ) ≤ 1
∑ P(x ) = 1
• Find the probability that the chosen student is not in the
traditional college age group (18 to 23).
1 − 0.57 = 0.43
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10/21/2014
Choose an American adult at random. Define two events:
A = the person has a cholesterol level of 240 mg per deciliter of blood (mg/dl)
or above (high cholesterol).
B = the person has a cholesterol level of 200 to 239 mg/dl (bordering high
cholesterol)
Homework
• Worksheet
According to the American Heart Association, P(A) = 0.16 and the P(B) = 0.29.
• Explain why events A and B are mutually exclusive.
A person cannot have a cholesterol level of both 240 or above and between 200 and 239 at the same time.
• What is P(A and B)?
0
• What is P(A or B)?
• If C is the event that the person chosen has normal cholesterol (below 200
mg/dl), what is P(C)?
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