How to transform this word problem into a binomial distribution equation

In summary, the airline sells 125 tickets for a flight that holds 120 passengers, with a probability of 0.10 that a passenger will not show up. The probability that every passenger who shows up can take the flight is 0.9^120 * 0.1^5, and the probability that the flight departs with empty seats is 0.9^0 * 0.1^125.
  • #1
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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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  • #2
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)
 

1. How do I identify a word problem that can be transformed into a binomial distribution equation?

To identify a word problem that can be transformed into a binomial distribution equation, look for situations that involve a fixed number of trials with two possible outcomes, success and failure. Examples can include coin tosses, yes/no questions, and pass/fail tests.

2. What are the key elements of a binomial distribution equation?

The key elements of a binomial distribution equation are the number of trials (n), the probability of success in each trial (p), and the number of successes (x) that are being counted.

3. How do I calculate the probability of a specific number of successes using a binomial distribution equation?

To calculate the probability of a specific number of successes (x) using a binomial distribution equation, you can use the formula P(x) = (nCx) * p^x * (1-p)^(n-x), where nCx represents the number of ways to choose x items from a set of n items. Alternatively, you can use a binomial probability calculator or table to find the probability value.

4. Can a binomial distribution equation be used to calculate the probability of a range of successes?

Yes, a binomial distribution equation can be used to calculate the probability of a range of successes. To do this, you would need to find the individual probabilities for each possible number of successes within the range and then add them together.

5. Are there any assumptions or limitations when using a binomial distribution equation?

Yes, there are a few assumptions and limitations when using a binomial distribution equation. These include the assumption that each trial is independent of the others, the assumption of a fixed number of trials, and the limitation that the probability of success remains constant throughout all trials.

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