### Binomial Experiment Probability CalculationIn this exercise, we will explore how to determine the probability of a certain number of successes in a binomial experiment. Here is the problem setup and instructions for Part 1 of the exercise.#### Problem SetupA binomial experiment is defined by:- The number of trials, $n$.- The probability of success in each trial, $p$.Given the parameters:- $n = 10$ (number of trials)- $p = 0.2$ (success probability for each trial)#### Instructions**Part 1 of 3:**(a) **Determine the Probability $P(2)$:** Calculate the probability of exactly 2 successes in 10 trials and round your answer to at least three decimal places.\[ P(2) = \]**Note:** No graphs or diagrams are provided in this part of the question. Simply input the calculated probability value.Use the following binomial probability formula for calculation:\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]Where:- $ \binom{n}{k} $ is the binomial coefficient.- $ k $ is the number of successes.**Example Calculation:**For $ n = 10 $, $ p = 0.2 $, and $ k = 2 $:\[ P(2) = \binom{10}{2} (0.2)^2 (0.8)^8 \]Ensure your answer reflects a rounded value to at least three decimal places before inputting it into the provided box.

n = 10 p = 0.2 q = 1- p = 1- 0.2 = 0.8

Answered: (a) Determine the probability P (2).

Math

Statistics

(a) Determine the probability P (2).

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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