UNIT 5: PROBABILITY
Basic Probability
Sample Space
Set of all possible outcomes for a chance experiment.
Example: Rolling a Die
Probability Model
• It is a description of some chance process
that consists of two parts
• A sample space (S)
• A probability for each outcome
Tree Diagram
A technique for listing the outcomes in a sample space. It
contains branches showing what can happen on different
trials.
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.
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
A = both tails
B = at least one head
Find P(A)
P(B)
Basic Rules of Probability – (don’t write yet)
•
Complement
•
Mutually Exclusive (Disjoint)
• Two events are mutually exclusive (disjoint)
if they have no outcomes in common and
so can never occur together.
Basic Probability Rules
•
Find the probability:
• Rolling a 5
• Choosing a girl in this class
• Drawing a king
Two marbles are pulled from a bag holding one
red, one white, one blue, and two green marbles.
A={the blue marble is drawn}
B={a green 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.
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.
• Find the probability that the chosen student is not in the
traditional college age group (18 to 23).
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)
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.
• What is P(A and B)?
• What is P(A or B)?
• If C is the event that ther person chosen has normal cholesterol
(below 200 mg/dl), what is P(C)?
Homework