Algebra 2B Day 43
12.6 Binomial Distributions
· Daily Openers
· Go over and collect homework
12.6 Binomial Distributions
binomial experiment – three features:
· situation involves repeated trials
· each trial has 2 possible outcomes (success or failure)
· the probability of success is constant throughout the trials (the trials
are independent)
Binomial Probability
For 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:
Ex. Suppose you were taking a 10 question True/False quiz. What is the probability of
getting 3 correct answers?
Ex. You buy a lottery ticket and it says 1 in every 4 are winners. If you buy 12 lottery tickets,
what is the probability that 3 will be winners?
Ex. If you would have bought 8 tickets, what is the probability that 2 would be winners?
Ex. Suppose you are taking a multiple choice quiz, and each question has 5 choices. The quiz
has 20 questions. What is the probability of getting 14 of the questions correct? What is the
probability of getting 12 correct?
Binomial Distribution
To find the full probability distribution, expand the binomial (p – q)n using Pascal’s ∆.
§ Show Pascal’s ∆ and binomial expansion.
§ Show the expansion for: (p – q)1, (p – q)2, (p – q)3, and (p – q)4
Ex. Show the full probability distribution for the binomial experiment. You take a 5 question
multiple choice quiz, with each question having 4 choices. What is n? What is p?
What is q?
Ex. What is the probability of getting at least 1 correct answer?
Ex. What is the probability of getting at least 2 correct answers?
Homework – Worksheet 12.6
Daily Openers – 1.–5. page 691 #42, 48, 3, 4, 7