Calculating Chances of Success with Binomial Distribution: A Homework Example

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SUMMARY

The discussion focuses on calculating the probability of achieving a specific outcome using the Binomial Distribution. The user has a 20% success rate (x = 0.2) and 6 attempts (n = 6) to achieve the desired result. The correct approach involves calculating the probability of getting 'x' at least once, which can be derived by first determining the probability of failing all attempts (P = (0.8)^6) and then subtracting this from 1. The initial attempt at using factorials was incorrect, as the user misapplied the formula.

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  • Understanding of Binomial Distribution
  • Familiarity with probability concepts
  • Basic knowledge of factorial notation
  • Ability to perform exponentiation
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  • Learn how to calculate probabilities using the Binomial Distribution formula
  • Study the concept of complementary probabilities in probability theory
  • Explore examples of Binomial Distribution applications in real-world scenarios
  • Review factorial calculations and their significance in probability
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Homework Statement


I am trying to figure out if I have a 20% chance to get what I want (let it = x) and I have 6 chances to do so (n=6), I am curious how I set this question up to find out my chances of getting 'x' once out of the 6 times I try.

Homework Equations


Binomial Distribution.

x! / y!(x - y)!


The Attempt at a Solution



x = 0.2
y = 0.8

= 0.8! / 0.2! (0.8 - 0.2)!
= 40320 / 1440
= 28

Any help would be appreciated.
 
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I don't think you quite get the binomial distribution. What is '.8!' suppose to mean? You might want to review it. On the other hand, the easy way to solve this problem is to figure out your odds of losing 6 straight times, call it P. Then your odds of winning are 1-P.
 

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