BINOMIAL DISTRIBUTION Success & Failures. Learning Goals I can use terminology such as probability distribution, random variable, relative frequency distribution,

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Presentation transcript:

BINOMIAL DISTRIBUTION Success & Failures

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.

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)

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.

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

Binomial Distribution

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.

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.

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

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.

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