Biostatistics with R/Some Basic Probability Concepts

Formular with R

Formular Number	Name	Formular	Formular with R
3.2.1	Classical probability	$P(E)=\frac{m}{N}$	Example
3.2.2	Relative frequency probability	$P(E)=\frac{m}{n}$	Example
3.3.1–3.3.3	Properties of probability	$P(E_i)\ge 0$ $P(E_1)+P(E_2)+\dots +P(E_n)=0$ $P(E_i+E_j)=P(E_i)+P(E_j)$	Example
3.4.1	Multiplication rule	$P(A\cap B)=P(A|B)P(B)=P(A)P(B|A)$	Example
3.4.2	Conditional probability	$P(A|B)=\frac{P(A\cap B)}{P(B)}$	Example
3.4.3	Addition rule	$P(A\cup B)=P(A)+P(B)-P(A\cap B)$	Example
3.4.4	Independent events	$P(A\cap B)=P(A)P(B)$	Example
3.4.5	Complementary events	$P(\bar{A})=1-P(A)$	Example
3.4.6	Marginal probability	$P(A_i)=\sum P(A_i\cap B_j)$	Example
	Sensitivity of a screening test	$P(T|D)=\frac{a}{(a+c)}$	Example
	Specificity of a screening test	$P(\bar{T}|\bar{D})=\frac{d}{(b+d)}$	Example
3.5.1	Predictive value positive of a screening test	$P(D|T)=\frac{P(D|T)P(D)}{P(T|D)P(D)+P(T|\bar{D})P(\bar{D})}$	Example
3.5.2	Predictive value negative of a screening test	$P(\bar{D}|\bar{T})=\frac{P(\bar{D}|\bar{T})P(\bar{D})}{P(\bar{T}|\bar{D})P(\bar{D})+P(\bar{T}|D)P(D)}$	Example
Symbol Key	$D$= disease $E$= Event $m$= the number of times an event E_i occurs $n$= sample size or the total number of times a process occurs $n$=Population size or the total number of mutually exclusive and equally likely events $P(\bar{A})$= a complementary event; the probability of an event A, not occurring $P(E_i)$=probability of some event E_i occurring $P(A\cap B)$=an “intersection” or “and” statement; the probability of an event A and an event B occurring $P(A\cup B)$=an “union” or “or” statement; the probability of an event A or an event B or both occurring $P(A|B)$=a conditional statement; the probability of an event A occurring given that an event B has already occurred $T$=test results		Example