### Probability Question: Knowledgeable Football Fans**Problem Statement:**Sixty-five percent of men consider themselves knowledgeable football fans. If 12 men are randomly selected, find the probability that exactly five of them will consider themselves knowledgeable fans.**Multiple Choice Options:**- A. 0.059- B. 0.204- C. 0.417- D. 0.650This question can be approached using the binomial probability formula, which is used to compute the probability of exactly $ k $ successes (in this case, five men considering themselves knowledgeable football fans) out of $ n $ trials (in this case, 12 randomly selected men), given the probability $ p $ of success on a single trial.#### Explanation of the Binomial Probability Formula:\[ P(X = k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k} \]Where:- $ n $ = 12 (number of trials)- $ k $ = 5 (number of successes)- $ p $ = 0.65 (probability of success)- $ \binom{n}{k} $ is the binomial coefficient, calculated as $ \frac{n!}{k!(n-k)!} $##### Steps to Calculate:1. **Calculate the Binomial Coefficient**: \[ \binom{12}{5} = \frac{12!}{5!(12-5)!} \]2. **Calculate the Probability**: \[ P(X = 5) = \binom{12}{5} \cdot (0.65)^5 \cdot (0.35)^7 \]Using these steps and probability calculations, one arrives at the final answer, which corresponds to one of the multiple-choice options provided.This problem serves as an excellent exercise in understanding how to apply binomial probability in practical scenarios and interpret statistical data accurately.

Answered: Image /qna-images/answer/200de128-0619-4cfd-97fa-a2cca5c277ab.jpg

Sixty-five percent of men consider themselves knowledgeable football fans. If 12 men are randomly selected, find the probability that exactly five of them will consider themselves knowledgeable fans. O A. 0.059 O B. 0.204 O C. 0.417 OD. 0.650

Sixty-five percent of men consider themselves knowledgeable football fans. If 12 men are randomly selected, find the probability that exactly five of them will consider themselves knowledgeable fans. O A. 0.059 O B. 0.204 O C. 0.417 OD. 0.650

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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