Homework Questions
Binomial Theorem
Binomial
 Bi – means 2 – two outcomes
 Win/lose, girl/boy, heads/tails
 Binomial Experiments
The following have to be true:
 The trials are independent
 Each trial has two outcomes
 P(S) or P(F)
 P(success) or P(failure)
 The probability of success is the same for
each trial. The probability of failure is 1-p
Ex 1
 In a basketball contest, each player is allowed
3 free-throws. If a certain individual has a 70%
chance of making each free-throw, what is the
probability of making exactly 2 out of 3?
Probability Formula
 In a binomial experiment,
P (r successes in n trials) = n Cr
r
pq
p = probability of success
q = 1-p is the probability of failure
n 1
Go back to #1
r
C
p
q
n r
2
3
n 1
1
C2 (.7) (.3)
Ex 2
 A lottery consists of choosing a number from
000 to 999. All digits of the number must be
matched in order, so the probability of
winning is 1/1000=.001. A ticket costs $1,
and the prize is $500. Suppose you play the
lottery 1000 times in a row.
 Write a probability distribution for the number of
wins
 What is the probability that you will break even?
a)
Outcome
Probability
0 wins 1 win
2 wins 3 wins
4 wins 5+ win
b)
Example 3
 Morgan is taking a 10 question multiple choice
test but has not studied. Each question has 4
possible responses, only one of which is
correct. Find the probability of getting the
results below if he answers all questions
randomly.




Exactly 6 questions correct.
4 or fewer questions correct.
8 or more questions correct.
Enough to pass…
Answers
a)
b)
c)
d)
Homework
 Worksheet