# Axioms of Probability: Cell Phone Factory

• noreturn2
In summary, there is a 10% chance that there is another issue with a cell phone, but this can only be determined by making assumptions about the mutually exclusive states of repaired and acceptable.
noreturn2

## Homework Statement

Give an factory of cell phones there is a .5 rejections, .2 repaired, and .2 acceptable. Does this follow the axioms of probability.

## Homework Equations

Sample space = 1;
Probaby: 0 -1
P(AnB)=P(A)+P(B)

## The Attempt at a Solution

Technically this does follow the axioms, there is just a 10% chance there is another issue of a board. Be it missing or something. Is that right?

It depends. If you say that 10% is neither accepted, rejected or repaired (so there is something else), you are correct.

If however there are only 3 possibilities (accept-reject-repair), you are wrong, since then ##\mathbb{P}(\Omega) = 0.9 \neq 1##.

Math_QED said:
Hint: the probability on the sample space must be 1. I.e., ##P(\Omega)=1##.

What is it in your case?

Well technically with how the question is worded it the sample space is accounted for. I guess we we assume there is only 3 conditions of a cell phone it's not accounted for. If we assume they there could be another option that wasn't listed it does account for 100% of the cases.

noreturn2 said:
Well technically with how the question is worded it the sample space is accounted for. I guess we we assume there is only 3 conditions of a cell phone it's not accounted for. If we assume they there could be another option that wasn't listed it does account for 100% of the cases.

Yes, I edited my post. Please have a look.

noreturn2 said:

## Homework Statement

Give an factory of cell phones there is a .5 rejections, .2 repaired, and .2 acceptable. Does this follow the axioms of probability.

## Homework Equations

Sample space = 1;
Probaby: 0 -1
P(AnB)=P(A)+P(B)

## The Attempt at a Solution

Technically this does follow the axioms, there is just a 10% chance there is another issue of a board. Be it missing or something. Is that right?

You must also make assumptions that, say, repaired and acceptable are mutually exclusive.

The question is badly worded, IMO. Simply quoting three numbers says nothing about the axioms of probability. It is mathematically imprecise.

## 1. What are axioms of probability?

The axioms of probability are a set of fundamental principles that govern the concept of probability. These axioms include the probability of an event being between 0 and 1, the sum of probabilities of all possible outcomes being equal to 1, and the probability of the union of two mutually exclusive events being equal to the sum of their individual probabilities.

## 2. How are axioms of probability applied in a cell phone factory?

In a cell phone factory, the axioms of probability are used to calculate the likelihood of various outcomes, such as the probability of a defective phone being produced or the probability of a specific model being chosen for production. These probabilities can then be used to make decisions and improve the efficiency of the factory's operations.

## 3. What is the importance of the axioms of probability in a cell phone factory?

The axioms of probability are crucial in a cell phone factory as they provide a mathematical framework for understanding and predicting the likelihood of different events. By applying these axioms, the factory can make informed decisions and improve their production processes, leading to increased efficiency and profitability.

## 4. How do the axioms of probability affect the quality of cell phones produced?

The axioms of probability can impact the quality of cell phones produced in a factory by helping to identify potential sources of defects and improving production processes. By accurately calculating probabilities, the factory can make adjustments and reduce the likelihood of producing faulty phones, resulting in higher quality products.

## 5. Can the axioms of probability be applied in other industries besides cell phone manufacturing?

Yes, the axioms of probability can be applied in various industries, such as finance, medicine, and insurance, to name a few. They provide a fundamental basis for understanding uncertainty and making informed decisions based on probabilities. In any industry where there is a need to predict and manage risk, the axioms of probability can be applied.

• Precalculus Mathematics Homework Help
Replies
4
Views
3K
• Set Theory, Logic, Probability, Statistics
Replies
10
Views
1K
• Precalculus Mathematics Homework Help
Replies
5
Views
1K
• Precalculus Mathematics Homework Help
Replies
4
Views
2K
• Precalculus Mathematics Homework Help
Replies
16
Views
2K
• Precalculus Mathematics Homework Help
Replies
7
Views
4K
• Precalculus Mathematics Homework Help
Replies
1
Views
1K
• Precalculus Mathematics Homework Help
Replies
8
Views
6K
• Precalculus Mathematics Homework Help
Replies
11
Views
2K
• Precalculus Mathematics Homework Help
Replies
9
Views
2K