## Ignorance gives one a large range of probabilities.

## – George Eliot

##### Source: Kakegurui

##### As a thrill junkie, I absolutely adore taking risks. That feeling of dread, your heart beating so fast that you can hear it drumming in your ear. Well, if you’re like me and Jabami Yumeko, you’d surely love this topic. Today, i’m here to discuss sets and probability. Enjoy!

##### Okay. So, before going to the fun part– probability, we’re going to discuss sets first. We need to understand sets first before going to probability to get a better view on the topic. *Title means “nowwww, let’s gamble, shall we? from the anime Kakegurui β₯οΈ

## In practical life, we are compelled to follow what is most probable; in speculative thought we are compelled to follow truth.

## – Baruch Spinoza

###### Source: Kakegurui

# πΊπ ππππ πππ ππππ?

#### A set is a group / collection of data. Each data in a set is called a member / element of the set. Ex: the set of all weebs in the world, the set of all apples on a tree, and the set of all numbers between 0 and 100.

#### When the elements of a set are listed, it is customary to enclose the list in curly brackets. For example, set N, all natural numbers between and including 5 to 10. Written as: K = {5,6,7,8,9,10}. Some of the common symbols used in sets:

###### source: https://www.kullabs.com/classes/subjects/units/lessons/notes/note-detail/2312

#### This is what it looks like when drawn in a Venn Diagram:

###### source: https://www.researchgate.net/figure/A-Venn-diagram-of-unions-and-intersections-for-two-sets-A-and-B-and-their-complements_fig1_3324531

#### A few terminology:

###### Source: http://subsurfwiki.org/wiki/Words_of_estimative_probability

####
For every action, there’s an infinity of outcomes. Countless trillions are possible, many milliards are likely, millions might be considered probable, several occur as possibilities to us as observers- and one comes true.

For every action, there’s an infinity of outcomes. Countless trillions are possible, many milliards are likely, millions might be considered probable, several occur as possibilities to us as observers- and one comes true.

## – China MiΓ©ville

# Now, finally!! To the fun part- π·ππππππππππ!

###### Source: Kakegurui

#### Probability is: the chance for something to happen. Formula:

###### Source: wiki how

##### Example: in a classroom of 24 students, 10 students watches Attack on Titan. The probability in this case is 5/12. This is because the total possible outcome is 24, since there are 24 space samples and 10 favorable outcomes. Simplify 10/24 = 5/12

## The concept of randomness and coincidence will be obsolete when people can finally define a formulation of patterned interaction between all things within the universe.

## – Toba Beta

###### Source: Kakegurui

# π»πππ π«ππππππ π³

##### In probability, tree diagrams may be used to represent a probability space. Tree diagrams may represent a series of independent events or conditional probabilities (will be explained later). Each node on the diagram represents an event and is associated with the probability of that event happening.

## I believe that we do not know anything for certain, but everything probably.

## – Christiaan Huygens

###### Source: Kakegurui

## Independent Event

##### Independent events are probability whose chances don’t change, whose chances stays the same. For example:

###### Source: https://www.onlinemathlearning.com/tree-diagram.html

##### Like in the example above, the chance of getting Head 3 times is 1/8 because 1/2 x 1/2 x 1/2. The probabilities for every coin being tossed is always 1/2.

## All statistics have outliers.

## – Nenia Campbell

###### Source: Kakegurui

## Conditional Probability

##### Probability of an event (A), given that another (B) has already occurred. Below is a formula to find the conditional probability of something:

###### Source: https://medium.com/@mithunmanohar/machine-learning-101-what-the-is-a-conditional-probability-f0f9a9ec6cda

##### Below is an example of a conditional probability question and how to solve it:

###### Source: https://m.youtube.com/watch?v=hR0fQ31-3lg

## The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.

## – Benoit Mandelbrot

###### Source: Kakegurui

# Real Life Application of Probability

## 1. Insurance Companies π₯ π

#### Probability helps in analyzing the best plan of insurance which suits you and your family the most. For example, you are an active smoker, and chances of getting lungs disease are higher in you. So, instead of choosing an insurance scheme for your vehicle or house, you may go for your health insurance first, because the chance of your getting sick are higher.

###### Source: Shigatsu Wa Kimi No Uso

## 2. Lottery Tickets π« π

#### In a typical Lottery game, each player chooses six distinct numbers from a particular range. If all the six numbers on a ticket match with that of the winning lottery ticket, the ticket holder is a Jackpot winner- regardless of the order of the numbers. The probability of this happening is 1 out of 10 lakh.

###### Source: https://gifer.com/en/7Emi

## 3. Gambling π°πΈ

#### Pretty much self explanatory. For example, when playing cards. There is a probability of getting a desired card when we randomly pick one out of 52. For example, the probability of picking up an ace in a 52 deck of cards is 4/52; since there are 4 aces in the deck. The odds of picking up any other card is therefore 52/52 β 4/52 = 48/52.

###### Source: Kakegurui

## Take the probability of loss times the amount of possible loss from the probability of gain times the amount of possible gain. That is what we’re trying to do. It’s imperfect, but that’s what it’s all about.

## – Warren Buffett

Thank You For Reading!!

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Although I am not a big fan of anime, I relly like how you integrated anime to maths. And I relly love the quotes you use. They are so relatable and relevant to the topic. Your first paragraph is a really good start and hooked me to read on rather than just skim through it. Consistency of pictures relating to the theme of anime you used is amazing. Real life example, especially the insurance companies was new for me. Thanks for sharing!

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