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% Document Info
\author{mariamaz}
\pdfinfo{
  /Title (wia2003-prob-stats-w1-w4.pdf)
  /Creator (Cheatography)
  /Author (mariamaz)
  /Subject (WIA2003 Prob\&Stats (W1-W4) Cheat Sheet)
}

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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{WIA2003 Prob\&Stats (W1-W4) Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{mariamaz} via \textcolor{DarkBackground}{\uline{cheatography.com/171452/cs/35985/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}mariamaz \\
  \uline{cheatography.com/mariamaz} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 29th April, 2024.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Probability and its notations}}  \tn
% Row 0
\SetRowColor{LightBackground}
Deterministic processes & outcome can be predicted exactly in advance \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
Random processes & outcome is not known exactly (can desc the probability distribution of possible outcomes) \tn 
% Row Count 8 (+ 5)
% Row 2
\SetRowColor{LightBackground}
Probability of event A & 0\textless{}=P(A)\textless{}=1 \tn 
% Row Count 10 (+ 2)
% Row 3
\SetRowColor{white}
Probability of whole sample space & P(S)=1, P(A)+P(B)+P(C) = 1 \tn 
% Row Count 12 (+ 2)
% Row 4
\SetRowColor{LightBackground}
Event A will almost definitely not occur & P(A)=0 \tn 
% Row Count 14 (+ 2)
% Row 5
\SetRowColor{white}
Only small chance that event A will occur & P(A)=0.1 \tn 
% Row Count 17 (+ 3)
% Row 6
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50-50 chance that event A will occur & P(A)=0.5 \tn 
% Row Count 19 (+ 2)
% Row 7
\SetRowColor{white}
Strong chance that event A will occur & P(A)=0.9 \tn 
% Row Count 21 (+ 2)
% Row 8
\SetRowColor{LightBackground}
Event A will almost definitely occur & P(A)=1 \tn 
% Row Count 23 (+ 2)
% Row 9
\SetRowColor{white}
Probability successful outcome (S) & P(S) = r/n ; r: num of successful outcomes, n: total num of equally likely outcomes \tn 
% Row Count 28 (+ 5)
% Row 10
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Permutations & Order is taken into account \tn 
% Row Count 30 (+ 2)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Probability and its notations (cont)}}  \tn
% Row 11
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Combinations & Order is not important \tn 
% Row Count 2 (+ 2)
% Row 12
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Permutation with repetition & n\textasciicircum{}r \tn 
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% Row 13
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Permutation without repetition & n!/(n-r)! \tn 
% Row Count 6 (+ 2)
% Row 14
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Combination with repetition & (r+n-1)!/r!(n-1)! \tn 
% Row Count 8 (+ 2)
% Row 15
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Combination without repetition & n!/(n-r)! \tn 
% Row Count 10 (+ 2)
% Row 16
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 & n: number of things to choose from ; r: them are chosen \tn 
% Row Count 13 (+ 3)
% Row 17
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Probability events A and B both occur & P(A∩B) \tn 
% Row Count 15 (+ 2)
% Row 18
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Events A and B are mutually exclusive or disjoint cannot occur at the same time & P\{A|B\}=0, P\{A∩B\}=0 \tn 
% Row Count 19 (+ 4)
% Row 19
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Probability events A or B occur & P(A∪B) \tn 
% Row Count 21 (+ 2)
% Row 20
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Conditional probability (event A occurs, given that event B has occured) & P(A|B) \tn 
% Row Count 25 (+ 4)
% Row 21
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Independent (event A does not change the probability of event B) & P\{A|B\} = P(A) \tn 
% Row Count 29 (+ 4)
% Row 22
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Complement (event that not occuring) & P(A') \tn 
% Row Count 31 (+ 2)
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Probability and its notations (cont)}}  \tn
% Row 23
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Rule of subtraction (event A will occur) & P(A) = 1 - P(A') \tn 
% Row Count 2 (+ 2)
% Row 24
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Rule of multiplication (probability of the intersection of two events) & P(A∩B) = P(A) x P(B|A) \tn 
% Row Count 6 (+ 4)
% Row 25
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Rule of addition (either event occurs, not mutually exclusive) & P(A∪B) = P(A) + P(B) - P(A∩B) \tn 
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% Row 26
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 & P(A∪B) = P(A) + P(B) - (P(A) x P(B|A)) \tn 
% Row Count 12 (+ 2)
% Row 27
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Random variable & determined by a chance event, outcome of a random experiment, measurable real-valued \tn 
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% Row 28
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Discrete random variable & range of X is finite ot countably infinite (values X can take on, not the size of the values) \tn 
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% Row 29
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Continuous random variable & range of X is uncountably infinite (that makes a physical measurement) \tn 
% Row Count 26 (+ 4)
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Bayes' Theorem}}  \tn
% Row 0
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Mutually exclusive/disjoint (if both events cannot occur together) & P(A∪B) = P(A)+P(B) \tn 
% Row Count 4 (+ 4)
% Row 1
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Collectively exhaustive (if at least one of the events must occur) & A∪B = S \tn 
% Row Count 8 (+ 4)
% Row 2
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Events A and B are independent & P(A∩B) = P(A) x P(B) \tn 
% Row Count 10 (+ 2)
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Events A and B are not independent & P(A∩B) = P(A) x P(B|A) \tn 
% Row Count 12 (+ 2)
% Row 4
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Conditional probability of A given B & P(A|B) = P(A,B) / P(B) \tn 
% Row Count 14 (+ 2)
% Row 5
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If A and B are statistically independent & P(A|B) = (P(A) x P(B)) / P(B) = P(A) \tn 
% Row Count 16 (+ 2)
% Row 6
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if A and B are statistically dependent & P(A|B) != P(A) \tn 
% Row Count 18 (+ 2)
% Row 7
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Multiplication rule for conditional probabilities & P(A∩B) = P(B) x P(A|B) or P(A∩B) = P(A) x P(B|A) \tn 
% Row Count 21 (+ 3)
% Row 8
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Bayes Theorem & P(A|B) = (P(B|A) x P(A)) / P(B) \tn 
% Row Count 23 (+ 2)
% Row 9
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 & P(S|F) = (P(F|S) x P(S)) / (P(F|S) x P(S)) + (P(F|S') x P(S')) \tn 
% Row Count 27 (+ 4)
% Row 10
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Prior probability & {\bf{originally}} obtained {\bf{before}} any additional information is obtained \tn 
% Row Count 31 (+ 4)
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Bayes' Theorem (cont)}}  \tn
% Row 11
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Posterior probability & has been {\bf{revised}} by using additional information that is {\bf{later}} obtained \tn 
% Row Count 4 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}