1. Binomial Probability Distribution
Consider the experiment in which a die is rolled three times. On each roll, the probability of getting a six (S) is 1/6 and the probability of getting a non-six (N) is 5/6. The tree diagram below summarizes the results of the experiment. S N
1/6
5/6
1/6
5/6
1/6
5/6
1/6
5/6
1/6
5/6
1/6
5/6
1/6
5/6
Now you fill in all of the other probabilities.
What is the p(3sixes)?
What is p(2 sixes)?

2. Binomial Probability Distribution
Outcomes: sixes sixes,1 non-six six,2 non-six sixes
Probability:
Compare to
Let’s define variables:
p = probability of a successful outcome,
q = probability of a failure, and
p + q = 1

3. Binomial Probability Distribution
BPD may be used whenever the following criteria are met.
*The experiment consists of 2 possible outcomes. (p and q)
*The experiment has a fixed number of trials. (repeated n times)
*The trials are independent.
*The probability of success, p, is the same in each trial.

4. Ex 1: A multiple choice test contains 20 questions
Ex 1: A multiple choice test contains 20 questions. Each question has five choices for the correct answer. Only one of the choices is correct. What is the probability of making an 80% B- with random guessing?
n=20 r=16 p=.20 q=.80
P(16 correct) =
= 4845(6.5536x10^-12)(.4096)
WOW!!!

5. Ex2: In a survey of 1000 students in a school, 950 indicated that they were right-handed. Find the probability that AT LEAST one of four randomly chosen students from the school are LEFT-HANDED.
Technically speaking, this is not a binomial experiment because the sampling of the four students is done without replacement. In this experiment the probability of the 1st student being right-handed is 950/1000=.95. The probability that the 2nd student is right-handed is either 949/999 or 950/999 depending on whether the 1st student was right-handed. These two probabilities (as well as those for the 3rd and 4th student’s being right-handed) are so close to .95 that we will use the binomial probability theorem even though the theorem requires a constant probability.
using the Complement
P(at least 1 lefty) =
1-P(all right-handed)
=1-.815
=.185 or 18.5%