1) The document introduces the binomial probability formula used to calculate the probability of getting doubles when rolling a pair of dice multiple times. 2) It provides the formula: P(x) = (nCx)p^x(1-p)^(n-x) where n is the number of trials, p is the probability of success on each trial, and x is the number of successes. 3) An example calculates the probability of getting doubles 1 time out of 5 rolls as 0.401878 using the formula with n=5, p=6/36, and x=1.

1. Introduction If I were to roll a pair of dice 5
times…
What’s the probability I get
doubles…
1 time? 2 times? 3 times?
4 times? 5 times?
To answer these
questions,
We need this really cool
thing
The
Binomial Probability
Formula!

2. Formula
x n x
n xP(x) C p q 

Probability
of x
n number of
trials, choose x
Probability of
success raised
to the x power
Probabilty of
failure raised to
the n-x power

3. Formula Since q = 1-p, the formula can be
rewritten as:
x n x
n xP(x) C p (1 p) 
 

4. Formula
You need to input 3 numbers into this
formula to find the probability of x
number of x successes out of n trials:
► the number of trials n
► the probability of success, p
► x, the number of successes
x n x
n xP(x) C p (1 p) 
 

5. Remember The nature of a binomial experiment is
to have a specified number of trials
The probability of success, p, is the
same for every trial
x is the random variable and usually
the focus of the problem
x = {1, 2, 3, …, n}
If n = 5, then x may equal 0, 1, 2, 3,
4, or 5

6. Insight
In the binomial
probability formula, nCx
determines the number
of ways of getting x
successes in n trials,
regardless of order.

7. Example n=5, p = 6/36, x=1
P(1) = (5C1)(6/36)1(30/36)5-1
P(1) = (5)(1/6)1(5/6)4
P(1) = (5/6)(5/6)4
P(1) = (5/6)5 = .401878
If I were to roll a pair of dice 5
times…
What’s the probability I get
doubles… 1 time?
x n x
n xP(x) C p (1 p) 
 

8. CalculationTips n=5, p = 6/36, x=1
P(1) = (5C1)(6/36)1(30/36)5-1
P(1) = (5)(1/6)1(5/6)4
P(1) = (5/6)(5/6)4
P(1) = (5/6)5 = .401878
x n x
n xP(x) C p (1 p) 
 
Think of the
formula as
multiplying 3
numbers
Group (n-x)
Resolve combination
formula and exponents
before multiplying!
Since there are 36
possible outcomes
when rolling two, 6-
sided die, and 6 of
those outcomes are
doubles, then the
probability of success
is 6/36

9. Example n=5, p = 6/36, x=3
P(1) = (5C3)(6/36)3(30/36)5-3
P(1) = (10)(1/6)3(5/6)2
P(1) = (10)(1/216)(25/36)
P(1) = (10/216)(25/36)
= .03125
If I were to roll a pair of dice 5
times…
What’s the probability I get
doubles… 3 times?
x n x
n xP(x) C p (1 p) 
 

10. Thinkabout
If we were to find P(0),
P(1), P(2), P(3), P(4), and
P(5), what would the sum
of those probabilities be?