1. Homework: p. 216-217 #16, 17, 18, 28, 29  16. a).023 b).027 c) Part b d) Yes

2. Section 5.3 Binomial Probability Distributions

3. 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?

4. 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.

5. 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.

6. 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?

7. 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)

8. 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?

9. 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?

10. 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 x 3. The solution can be found under the column that matches your probability for success [p].

11. 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?

12. 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)

13. Other Options Your Saving Grace Your Toolbox  Press 2 nd 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.

14. 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.