Answered: 1) What is the probability Mr. Keller…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Finding Binomial Probabilities

Mr. Keller filled out a bracket for the NCAA National Tournament. Based on his knowledge of college basketball, he has a 0.64 probability of correctly picking the winner of a game in the tournament. The NCAA National Tournament has 32 first round games.

Round each answer to 3 decimal places.

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

2) What is the probability Mr. Keller will pick exactly 8 games correctly in the first round?

3) What is the probability Mr. Keller will pick exactly 26 games incorrectly in the first round?

Expert Solution

Step 1

The binomial probability distribution is,

$P (X = x) = (\begin{matrix} n \\ x \end{matrix}) {(p)}^{x} {(1 - p)}^{n - x}$

In the formula, n denotes the number of trails, p denotes probability of success, and x denotes the number of success.

Let X be the correctly picking the winner of a game in the tournament which follows binomial with sample size 32, and probability of success 0.64.

The probability Mr. Keller would pick all 32 of the first round games correctly is,

$\begin{array}{rcl} P (X = 32) & = & (\begin{matrix} 32 \\ 32 \end{matrix}) {(0.64)}^{32} {(1 - 0.64)}^{32 - 32} \\ = & 0.000 \end{array}$

Thus, the probability Mr. Keller would pick all 32 of the first round games correctly is 0.

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