Probability is a measure of how likely something is to happen. 
We may intuitively know that the probability of getting a tail from a fair coin toss is $50\%$ or $\frac{1}{2}$ but how do we calculate it? 
<div class="content-block content-block--table"><div class="table-container"><table><colgroup><col style="width: 100px;"><col style="width: 400px;"><col style="width: 100px;"></colgroup><thead><tr style="height: 43px;"><th style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start"></th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">Sample Space (Possible Outcomes)</th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">Probability</th></tr></thead><tbody><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">Tossing a coin<img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765275049427-vfy24ms5wy.png" data-width="75%" style="width: 75%; max-width: 75%;"></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765275091911-jcjkcyi6z6.png" data-width="25%" style="width: 25%; max-width: 25%;">Tail Head</td><td style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start; vertical-align: top">Probability of getting a head</td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center; vertical-align: top">Picking a card<img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765275194185-vl2a04nh5un.png" data-width="75%" style="width: 75%; max-width: 75%;"></td><td style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start"><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1769404058317-8t0ag9nc47k.png" data-width="50%" style="width: 50%; max-width: 50%;"></td><td style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start; vertical-align: top">Probability of getting an ace</td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">Tossing a die<img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765275292762-hsz45jqmn0h.png" data-width="50%" style="width: 50%; max-width: 50%;"></td><td style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start"><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765275307573-qb4webajew.png" data-width="50%" style="width: 50%; max-width: 50%;"></td><td style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start; vertical-align: top">Probability of getting an even number</td></tr></tbody></table></div></div>
In general, if there is $n$ equally likely outcomes, if&nbsp;$k$ of these outcomes that satisfies the event $A$, then the probability, $\mathrm{P}\left( A \right)$, of $A$ happening is given by:
${\mathrm{P}}(A) = \frac{k}{n} = \frac{\mathrm{Number\ of\ outcomes\ satisfying\ event\ } A}{\mathrm{Total\ number\ of\ possible\ outcomes}}$
For any event $A$, $0\le \mathrm{P}\left( A \right)\le 1$ or $0\%\le \mathrm{P}\left( A \right)\le 100\%$. 
•	$\mathrm{P}\left( A \right)=0$ if and only if event $A$ is an impossible event. 
•	$\mathrm{P}\left( A \right)=1$ if and only if event $A$ is a certain event.

**Probability** is a measure of how likely something is to happen. 

We may intuitively know that the probability of getting a tail from a fair coin toss is $50\%$ or $\frac{1}{2}$ but how do we calculate it?  

Sample Space (Possible Outcomes)

Tossing a coin<img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765275049427-vfy24ms5wy.png" data-width="75%" style="width: 75%; max-width: 75%;">

<img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765275091911-jcjkcyi6z6.png" data-width="25%" style="width: 25%; max-width: 25%;">Tail Head

Picking a card<img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765275194185-vl2a04nh5un.png" data-width="75%" style="width: 75%; max-width: 75%;">

Tossing a die<img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765275292762-hsz45jqmn0h.png" data-width="50%" style="width: 50%; max-width: 50%;">

Probability of getting an even number

In general, if there is $n$ equally likely outcomes, if $k$ of these outcomes that satisfies the event $A$, then the probability, $\mathrm{P}\left( A \right)$, of $A$ happening is given by:

${\mathrm{P}}(A) = \frac{k}{n} = \frac{\mathrm{Number\ of\ outcomes\ satisfying\ event\ } A}{\mathrm{Total\ number\ of\ possible\ outcomes}}$

For any event $A$, $0\le \mathrm{P}\left( A \right)\le 1$  or $0\%\le \mathrm{P}\left( A \right)\le 100\%$. 

•	$\mathrm{P}\left( A \right)=0$ if and only if event $A$ is an **impossible** event.  

•	$\mathrm{P}\left( A \right)=1$ if and only if event $A$ is a **certain** event.  

Basics of Probability of Single Events

Basics of Probability of Single Events

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