Part IV –Randomness and Probability
Ch. 17 – Probability Models
(Day 2 – The Binomial Model)
It’s still about
me!
The Binomial Distribution
• Still using Bernoulli trials
• For the geometric model, we were looking for
• For the binomial model, we are looking for
The Binomial Setting
Four requirements for a situation to follow a
binomial distribution:
•
•
•
•
(Note that these last three are the requirements
for Bernoulli trials)
1
Binomial Probability Formula
• X=
• n=
• p=
Ex 1 A coin is flipped four times. Find the
probability of getting exactly 2 heads.
The old way…
• HHHH
HHHT
TTHT
THHT
TTTT
TTTH
HTTH
THHH
TTHH
HHTT
HTHH
HTTT
HTHT
HHTH
THTT
THTH
• P(2 heads) =
• This is fine, but what if I had flipped the coin 20
times and asked the same question?
Using the formula
• First, let’s check to see if this is a binomial
setting (using the four requirements)…
• n=
• p=
2
• Ex 2 Kobe Bryant is an 84% free throw shooter.
He shoots 8 free throws in a particular game.
– What is the probability that he makes exactly 6?
– What is the probability that he makes at least 6?
– What is the probability that he makes at least two?
• Ex 3 A die is rolled 11 times. Find the
probability that a four is rolled at least 3 of
these times.
• Find the probability that a four is rolled on at
least 3 of 4 rolls
Don’t Forget
• Before you use the binomial probability
formula for a problem, make sure you first
check to see whether it is appropriate for that
situation! (Check the 4 requirements)
3
Mean and Standard Deviation of a
Binomial Random Variable
• When Kobe takes 8 shots in a game, how
many do we expect him to make on average?
• What is the standard deviation of the number
of shots made?
Homework
• p. 399 #13cdef,
#14 def, #15-20
4