1. BINOMIAL DISTRIBUTION Success & Failures

2. Learning Goals I can use terminology such as probability distribution, random variable, relative frequency distribution, etc. I can provide an example of a Bernoulli trial, Binomial experiment, and a Binomial Distribution. I can give examples of situations where a binomial distribution exists. I can list the five criteria that makes for a binomial experiment, and thus a binomial distribution. I can state and use the formula for a binomial distribution. I can state and use the expected value formula for a binomial distribution.

3. Investigation Investigation: A die is rolled 3 times. The number of 5’s that appear is recorded. Create a probability distribution table for the number of 5’s that could appear. Let X = the number of 5’s rolled XP(X)

4. Investigation continued… What patterns do we notice in each probability? This situation can be modeled as a success and failure, where “success” is getting a 5 and “failure” is not getting a 5. This is known as a Bernoulli trial.

5. Bernoulli Experiment A Bernoulli experiment is any experiment that meets the following criteria: There are n identical trials There are two possible outcomes for each trial: Success – usually denoted as p Failure – usually denoted as q = 1- p The values of p and q do not change from trial to trial. The trials are independent

6. Binomial Distribution

7. Back to the Investigation… Using the formulas, let’s go back to the investigation and determine the following: a) the probability of rolling two 5’s. b) the expected value.

8. Example #1 A set of 4 regular dice are rolled. The number of times a 3 appears is recorded. a) Explain how this situation meets the requirements for a binomial experiment. b) Create a probability distribution table for this experiment. c) Find the expected number of 3’s.

9. Homework Day #1 Work: page 299 #1, 2, 6, 7, 8

10. Example #2 The Chocoholics Candy Company makes chocolate covered candies. The production line mixes the candies randomly and packages 10 per box. It is know that 40% of all candies made are red. a) What is the probability that at least 2 candies in a given box are red? b) Determine the expected number of red candies in a box.

11. Homework Day #1 Work: page 299 #1, 2, 6, 7, 8 Complete this if you did not the night before. No sense in moving on to harder questions if you didn’t attempt the first set. Day #2 Work: page 301 #9, 10, 12, 13, 16