Binomial Distribution: Finding Probability with Trials, Success, and X Value

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  • #1
TyErd
299
0

Homework Statement


I've uploaded a picture of the question.
I need help in identifying the correct number of trials, probability of success and the X value(number of successes)

Homework Equations


i'm using the binomial distribution function on the calculator but I've attached the formula just in case

The Attempt at a Solution


I used n=7, p=7/15 and X=7 which yields me a probability of 0.00482 which is incorrect. The correct answer is 0.000155 but not sure how.
 

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  • #2
TyErd said:

Homework Statement


I've uploaded a picture of the question.
I need help in identifying the correct number of trials, probability of success and the X value(number of successes)

Homework Equations


i'm using the binomial distribution function on the calculator but I've attached the formula just in case


The Attempt at a Solution


I used n=7, p=7/15 and X=7 which yields me a probability of 0.00482 which is incorrect. The correct answer is 0.000155 but not sure how.

The binomial distribution is inappropriate for this problem. You aren't doing independent trials with replacement. Think about how many ways you can select 7 cars from the 15 and how many ways you can select the 7 fwd cars.
 
  • #3
That's not a correct formula to use. How many ways are there to choose 7 cars from 15? Only one of those choices gives you all four wheel drives.
 
  • #4
ahh, that's why i keep getting it wrong. Thanks, but if its not binomial, what is it?
 
  • #5
It's combinatorics. How many ways to select 7 objects from 15 objects?
 
  • #6
TyErd said:
ahh, that's why i keep getting it wrong. Thanks, but if its not binomial, what is it?

It is the so-called hypergeometric distribution.

Note: instead of a combinatorial argument there is another way to get the correct answer. The probability that the first car is fwd is 7/15; that leaves 14 cars, of which 6 are fwd. So (given the first is fwd) the probability that the second is fwd is 6/14, etc, etc.

RGV
 

What is a binomial distribution?

A binomial distribution is a probability distribution that describes the likelihood of a certain number of successes in a fixed number of independent trials, with a given probability of success for each trial.

What is the formula for calculating binomial probability?

The formula for calculating binomial probability is P(x) = (nCx)(px)(qn-x), where n is the number of trials, x is the number of successes, and p is the probability of success for each trial. q is equal to 1-p, the probability of failure.

How do you use the binomial distribution to find probability?

To use the binomial distribution to find probability, you need to know the number of trials, the probability of success for each trial, and the desired number of successes. Plug these values into the binomial probability formula, P(x), and solve for the probability P(x).

What is the difference between a binomial distribution and a normal distribution?

A binomial distribution is used to model discrete data, where there are a specific number of outcomes (e.g. number of heads in 10 coin flips). A normal distribution, on the other hand, is used to model continuous data, where there is an infinite number of possible outcomes (e.g. height or weight).

What are some real-life applications of the binomial distribution?

The binomial distribution can be used to model real-life situations such as coin flips, test scores, and election results. It is also commonly used in quality control and market research.

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