How to transform this word problem into a binomial distribution equation

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SUMMARY

This discussion focuses on transforming a word problem related to airline ticket sales into a binomial distribution equation. The problem states that an airline sells 125 tickets for a flight with a capacity of 120 passengers, with a 10% no-show probability. The solutions provided utilize the binomial formula f(x) = n nCr x p^x(1 - p)^(n-x) to calculate the probability that all passengers who show up can take the flight and the probability of empty seats on departure.

PREREQUISITES
  • Understanding of binomial distribution and its properties
  • Familiarity with combinatorial mathematics, specifically nCr (combinations)
  • Knowledge of probability concepts, particularly independent events
  • Ability to apply the binomial probability formula in practical scenarios
NEXT STEPS
  • Study the application of the binomial distribution in real-world scenarios
  • Learn how to calculate probabilities using the binomial formula in various contexts
  • Explore advanced topics in probability theory, such as the Poisson distribution
  • Practice solving similar word problems involving binomial distributions
USEFUL FOR

Students studying probability and statistics, educators teaching binomial distributions, and anyone preparing for exams involving combinatorial mathematics.

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Homework Statement


Because not all airline passengers show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 120 passengers. The probability that a passenger does not show up is 0.10, and the passengers behave independently

a) What is the probability that every passenger who shows up can take the flight?
b) What is the probability that the flight departs with empty seats?


Homework Equations



f(x) = n nCr x p^x(1 - p)^n-x

The Attempt at a Solution



a) 125 nCr 120 (0.9)^120*(0.1)^5

b) 125 nCr 0 (0.9)^0 * (0.1)^125
 
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let n be the number of passengers and p be the probability they won't turn up.
(a)find prob less than or equal to 5 don't turn up
(b)similar thing as (a)
 

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