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)