Binary Probability

In mathematics there is a whole theory of probability. Some examples of probability are like, what is the probability of rolling two 6′s on two 6 sided dice? The answer would be $\frac{1}{36}$ . You have a $\frac{1}{6}$ chance to roll a 6 on each dice, so $\frac{1}{6} \times \frac{1}{6} = \frac{1}{36}$ . Now… what if I were to tell you that this is wrong…

The concept I have thought of is binary probability. The name because of the answer being either a yes or a no, a 1 or a 0, etc.

Think about it, everything either happens or it doesn’t. “Hmm, am I going to win the lottery today?” Well, that question could be a yes or a no, meaning you have a 50/50 shot at winning it. Sounds simple right? Well it is…

Now we will go into some definitions and the main theorem of the idea.

Definition: Binary Question – A logical query that has two possible outcomes.

Some examples are as such: Do I need gas in my car? Can I do a backflip? Can I splice the genes from a chihuahua into a kumquat? Each one of these questions have a simple yes or no answer.

Theorem 1: In every Binary Question, the probability of each event happening is .5.

Proof:
Assume we are not in a quantum space.
Assume you have a Binary Question, $a \in A$ , where $A$ is the set of all Binary Questions.
$a$ can have two outcomes by definition, $a_1$ and $a_2$ .
Only one of the outcomes in the Binary Question can happen seeing as we are not in a quantum space.
so, $\frac{1}{2} = .5$ which is 50%.
$Q.E.D.$

Now, you may ask the question, what about a multiple choice question? Simple. Theorem 1 can be expanded to a n-choice question without even thinking twice.

Definition: $n$ -choice question: A $n$ -choice question is a question that could have $n$ answers to it, where $n \ge 2$ and $n \le \infty$ .

Example: How many fish are in the fish tank?

Well… Are there 3 fish in the tank? Either yes or no, 50% chance. 4 fish? Yes or no, 50% chance. 5 fish? Yes or no, 50% chance, etc.

By definition, a Binary Question is a special case of a $n$ -choice question, where $n = 2$ .

Now, we’ll expand out Theorem 1 into another theorem, a more generalized version of the theorem to show the true power of Binary Probability.

The Main Theorem of Binary Probability
Each event of a $n$ -choice question has a .5 probability of happening.

Proof:
Assume you have a $n$ -choice question, $b \in B$ where $B$ is the set of all $n$ -choice questions.
$\forall b \in B,$ $b$ has $n$ Binary Questions, $c_1, c_2,\ldots , c_n$
By Theorem 1, we know that every choice of a Binary Question has a .5 probability of happening.
So, $\forall c_1, c_2,\ldots , c_n$ , $c_n$ has a .5 probability of happening.
$Q.E.D$

2009: 12/01
CATEGORY: Math
TAGS: 0
1
Binary
Math
Probability
satire
3 comments

- Professor X
- December 1st, 2009
- REPLY
- QUOTE
Why would you do this to me!
- BernieR
- December 4th, 2009
- REPLY
- QUOTE
Interesting, did you plan to continue this article?
BernieR
- SaumZ
- December 14th, 2009
- REPLY
- QUOTE
I might think about doing more satirical math articles I think it’s fun to write them. This was also an exercise for me to play with the wordpress latex plugin

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December 14th, 2009

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What the %&#$ is Wrong?

Binary Probability

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