# Calculating Binomial Probability for Car Color Preferences

• tzx9633
In summary, the conversation discusses using binomial probability to find the probabilities of a certain number of black cars in a sample of 20 randomly selected cars. The correct approach is to find P(3 ≤ x ≤ 5) and the given answer is 0.312.
tzx9633

## Homework Statement

Car colour preferences changes over year . In this year , suppose that 10% of the car are randomly selected , let the sample of cars are 20 . Find the probabilities between thre and five cars ( inclusive ) are black ...

I am aksed to do this question using binomial .

## The Attempt at a Solution

I treated it as P ( 3 < x ≤ 5 ) , am i right ?
so , P( x = 4) + P ( x = 5)
=
(20c4) ((0.1)^4) ( 0.9^16) + (20c5) ((0.1)^5) ( 0.9^15) = 0.1217 ,

However , the ans given is = 0.312 , which part of my working is wrong ?

tzx9633 said:
I treated it as P ( 3 < x ≤ 5 ) , am i right ?
so , P( x = 4) + P ( x = 5)
=
(20c4) ((0.1)^4) ( 0.9^16) + (20c5) ((0.1)^5) ( 0.9^15) = 0.1217 ,

It is supposed to be P( 3 ≤ x ≤ 5 ). For some reason you treated the '5' correct but not the '3'.

So it will be P( x = 3) + P (x = 4) + P ( x = 5 ) = 0.312

solved !

## 1. What is binomial probability?

Binomial probability is a mathematical concept that calculates the likelihood of a certain number of successful outcomes in a series of independent trials or experiments. It is used to understand and predict the probability of a specific event occurring.

## 2. How is binomial probability calculated?

Binomial probability is calculated using the formula P(x) = nCx * p^x * (1-p)^(n-x), where n is the number of trials, x is the number of successful outcomes, and p is the probability of success in each trial. The nCx is the combination formula for choosing x objects from a set of n objects.

## 3. How can binomial probability be applied to car color preferences?

Binomial probability can be used to determine the likelihood of a specific car color being preferred by a certain number of individuals in a given population. For example, if 70% of a population prefers red cars and a sample of 100 people is taken, binomial probability can be used to calculate the probability of exactly 70 people preferring red cars.

## 4. What factors can affect binomial probability in car color preferences?

Some factors that can affect binomial probability in car color preferences include cultural trends, marketing tactics, and personal preferences. These factors can influence the probability of a certain car color being preferred by individuals in a given population.

## 5. How can binomial probability be used in decision making for car manufacturers?

Car manufacturers can use binomial probability to understand the preferences of potential customers and make decisions about which car colors to produce in larger quantities. By analyzing the probability of certain car colors being preferred, manufacturers can make strategic decisions to meet consumer demands and increase sales.

• Calculus and Beyond Homework Help
Replies
4
Views
1K
• Calculus and Beyond Homework Help
Replies
10
Views
2K
• Calculus and Beyond Homework Help
Replies
7
Views
1K
• Calculus and Beyond Homework Help
Replies
7
Views
1K
• Calculus and Beyond Homework Help
Replies
5
Views
1K
• Calculus and Beyond Homework Help
Replies
3
Views
1K
• Calculus and Beyond Homework Help
Replies
2
Views
3K
• Calculus and Beyond Homework Help
Replies
13
Views
7K
• Calculus and Beyond Homework Help
Replies
6
Views
2K
• Calculus and Beyond Homework Help
Replies
4
Views
1K