#### Chapter 15 Notes

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Transcript Chapter 15 Notes

Binomial
Distribution
(Dr. Monticino)
Assignment Sheet
Read Chapter 15
Assignment # 9 (Due March 30th)
Chapter 15
Exercise Set A: 1-6
Review exercises: 1,2,3,4 (important),5,6,7,10,11
Re-do example problems in last two lectures
Exam 2 is projected to be on April 11th or 13th
depending on when we finish Chapter 18
Overview
Binomial Model
Assumptions
Calculating Probabilities
Examples
Law of Averages
Binomial Model
The binomial distribution is used as a model
for a process which is repeated n times.
Each time the process is repeated,
outcomes are classified as either successes
or failures
Each time the process is repeated there is
the same probability of a success occurring
Successive outcomes are independent of
one another
Binomial Distribution
Under the assumptions of the binomial
model, the probability of k successes out of n
repetitions is
n k
n k
p (1 p)
k
Examples
Flip a fair coin 10 times
What is the probability that 10 heads come
up?
What is the probability that exactly 8 tails
occur?
What is the probability that at least 8 tails
occur?
Examples
Roll two fair die 5 times
What is the probability that 5 “doubles”
are rolled?
What is the probability that doubles are
rolled at most twice
What is the probability that the sum of the
die is seven on 3 out of the 5 rolls
Examples
The likelihood of a women developing
breast cancer during her lifetime is 1 in 9
Suppose 8 women are randomly chosen
from the population
What is the probability that they all develop
breast cancer
What is the probability that at least two will
develop breast cancer?
Law of Averages
The law of averages says that if a chance
process is repeated a large number of times ,
then the percentage of times that a particular
event occurs is likely to be close to the
probability of that event
Provided the assumptions assumed for the
binomial model hold
There is always chance error
(Dr. Monticino)