Homework: p. 216-217 #16, 17, 18, 28, 29

16. a) .023b) .027c) Part bd) Yes

Section 5.3

Binomial Probability Distributions

Homework Quiz

On Deal or No Deal there is an equal chance of ending up with a case valued at $0.01, $1, $5, $10, $25, $50, $75, $100, $200, $300, $400, $500, $750, $1000, $5000, $10000, $25000, $50000, $75000, $100000, $200000, $300000, $400000, $500000, $750000, and $1000000. What is the expected value of your earnings if you decide to pick 1 case and stick with it?

Binomial Probability Distribution

What is it? Requirements:

A Binomial Probability Distribution is a special kind of probability distribution that results from a procedure that meets a specific set of requirements.

1. The procedure has a fixed number of trials.

2. The trials are independent

3. Each trial can either be a success or a failure.

4. The probability of success/failure remains consistent through each trial.

Helpful Rule for Independence

Remember:However:

Two events are independent if one event occurring doesn’t affect the probability of the other event.

This is an issue if you are dealing with no replacement.

If your sample size represents less than 5% of the

total population, you can treat the events as if they are independent.

Example

Consider an experiment in which 5 offspring peas are generated from 2

parents such that there is a 75% chance of an individual pea having a

green pod and a 25% chance of it having a yellow pod.

Is this a Binomial Probability Distribution?

A formula for Calculating Probability

The Formula The Components

n: the number of trials

x: the number of successful trials

p: the probability of success

q: the probability of failure ( q = 1 – p)

Example

Consider the earlier experiment in which 5 offspring peas are generated

from 2 parents such that there is a 75% chance of an individual pea having a green pod and a 25%

chance of it having a yellow pod.

What’s the probability of getting exactly 3 offspring peas with green

pod’s?

Example

McDonald’s has a brand name recognition rate of 95%. Assuming that we randomly select 5 people, what is the probability that exactly 3 of the 5 have heard of McDonald’s?

Using Tables

Binomial probability can be calculated without a calculator or formula. Our book has a binomial distribution table that can be used to quickly find the probability given the specific parameters. Located on p. 749

1. Start by locating your value for n on the far left side of the table

2. Move to the line that matches your value of x3. The solution can be found under the column

that matches your probability for success [p].

Example

Use your table to find the solution to the revised problem below.

McDonald’s has a brand name recognition rate of 95%. Assuming that we randomly select 5 people, what is the probability that at least 3 of the 5 have heard of McDonald’s?

Pros and Cons for Tables

Pros Cons

Quicker Good for having to

do several calculations with very little change concerning the inputs

Limited number of inputs, so not always an option.

Not as much information (all numbers are pre-rounded)

Other Options

Your Saving Grace Your Toolbox

Press 2nd VARS (to get DISTR), then select the option identified as binompdf.

Complete the entry of binompdf(n, p, x) with specific values for n, p, x, then press ENTER.

1. Use a TI-83/84 Plus. 2. Use the Table A-1.

Homework

Pg. 225: 5-8, 15, 16, 21-22, 31, 36

Helpful hint: The probability of “at least” is the same as 1

minus the probability of LESS than that number.

For example if there are 5 options (1, 2, 3, 4, 5) the probability of at least 2 is 1 minus the probability of 1.