# Introduction to Decision Analysis 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)