# Axioms of Probablity

## 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?

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Math_QED
Homework Helper
2019 Award
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 $\mathbb{P}(\Omega) = 0.9 \neq 1$.

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.

Math_QED
Homework Helper
2019 Award
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.

PeroK
Homework Helper
Gold Member

## 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.