# Probability of Guessing game outcome

1. Feb 23, 2016

### RyanTAsher

1. The problem statement, all variables and given/known data

Mr. Keller filled out a bracket for the NCAA national tournament, based on his knowledge of college basketball, he has a .61 probability of guessing any one game correctly.

What is the probability Mr. Keller will pick all 32 of the first round games correctly?

2. Relevant equations

Binomial distribution?

3. The attempt at a solution

This class is a calculator course, so I don't know any of the algebraic theory, but I try to plug it into my binomialpdf on my calculator and it's not coming out correctly, how would I calculate this?

2. Feb 23, 2016

### SammyS

Staff Emeritus
What buttons on your calculator have you been taught to press?

3. Feb 24, 2016

### RUber

The binomial distribution looks something like:
if x is the number of correct guesses and p is the probability of a correct guess, then the probability of x correct guesses out of n tries P(x) can be written:
*edited, thank you to Ray for pointing it out*
$P(x) =\left( \begin{array}{c} n \\ x \end{array}\right) p^x(1-p)^{n-x}$
Your input for the calculator might be something like shown here where you input [n= number of trials, p=probability of correct, x = #correct].
If the output is anything close to correct, it would be the same as if you calculated the formula for P(x).
In this case, it should give something near $10^{-7}$.

Last edited: Feb 24, 2016
4. Feb 24, 2016

### Ray Vickson

The formula above is wrong; it should be
$$P(x) = {n \choose x} p^x \, (1-p)^{n-x},$$
where ${n \choose x}$ is the binomial coefficient "n choose x".