Essential Question: Why, for a binomial probability, p + q must

equal 1

Unit: Probability12-6: Binomial Distributions

12-6: Binomial DistributionWrite your name on a piece of paperMake two columns

Number each column 1 – 6DO NOT DISCUSS YOUR ANSWERS WITH

YOUR NEIGHBORS – you will mess up this experimentIn the first column, for questions 1 – 6,

answer “T” or “F”In the second column, for questions 1 – 6, answer “A”, “B”, “C”, or “D”

Exchange your paper with a partner for them to grade

12-6: Binomial Distribution Answers

(T/F)Answers (A/B/C/D)

1 F D

2 T B

3 F C

4 F C

5 T B

6 F A

12-6: Binomial DistributionA binomial experiment has three important features:

1) The situation involves repeated trials2) Each trial has two possible outcomes

Success or failure

3) The probability of success is constant throughout the trials

The trials are independent

Suppose you have repeated independent trials, each with a probability of success p and a probability of failure q (with p + q = 1). Then the probability of x successes in n trials is the following product:

nCxpxqn-x

12-6: Binomial DistributionSuppose you guess the answer to six

questions on a true or false test. What is the probability of you passing the test?What is the probability of success?

What is the probability of failure?

What are the situations where you pass?

Find the probability of 4/5/6 correct answers out of 6 questions

So the probability of you passing is

50%, or 0.5

4, 5 or 6 correct

50%, or 0.5

6C6 • .56 • .50 = 0.015625

6C5 • .55 • .51 = 0.09375

6C4 • .54 • .52 = 0.234375

0.234375 + 0.09375 + 0.015625 = 0.34375, or 34.4%

12-6: Binomial DistributionWhat if the test was multiple choice test with

four possible answers. What is the probability of you passing the test?What is the probability of success?

What is the probability of failure?

What are the situations where you pass?

Find the probability of 4/5/6 correct answers out of 6 questions

So the probability of you passing is

25%, or 0.25

4, 5 or 6 correct

75%, or 0.75

6C6 • .256 • .750 ≈ 0.00024

6C5 • .255 • .751 ≈ 0.00439

6C4 • .254 • .752 ≈ 0.03296

0.03296 + 0.00439 + 0.00024 = 0.03759, or 3.8%

12-6: Binomial DistributionA calculator contains 4 batteries. With

normal use, each battery has a 90% chance of lasting one year. What is the probability that all four batteries will last a year?What is the probability of success?

What is the probability of failure?

Find the probability of 4 out of 4 lasting

batteries

90%, or 0.90

10%, or 0.10

4C4 • .904 • .100 = 0.6561, or 65.61%

12-6: Binomial DistributionAssignment

Page 688 – 689Problems 1 – 14, allIgnore the directions:

For #1 – 3, find the theoretical probability instead of the experimental

For #4 – 7, don’t worry about the tree diagramFor #12 – 14, find all breakdowns for n = 6 (including

when x = 0)

Plan for the weekMonday, 12-6Tuesday, 12-3Wednesday, Test PreviewThursday, Probability Test