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 
$P(E_{i})\geq 0$
$P(E_{1})+P(E_{2})+\dots +P(E_{n})=0$
$P(E_{i}+E_{j})=P(E_{i})+P(E_{j})$

Example

3.4.1 
Multiplication rule 
$P(A\cap B)=P(AB)P(B)=P(A)P(BA)$ 
Example

3.4.2 
Conditional probability 
$P(AB)={\frac {P(A\cap B)}{P(B)}}$ 
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 
$P({\overline {A}})=1P(A)$ 
Example

3.4.6 
Marginal probability 
$P(A_{i})=\sum {P(A_{i}\cap B_{j})}$ 
Example


Sensitivity of a screening test 
$P(TD)={\frac {a}{(a+c)}}$ 
Example


Specificity of a screening test 
$P({\overline {T}}{\overline {D}})={\frac {d}{(b+d)}}$ 
Example

3.5.1 
Predictive value positive of a screening test 
$P(DT)={\frac {P(DT)P(D)}{P(TD)P(D)+P(T{\overline {D}})P({\overline {D}})}}$ 
Example

3.5.2 
Predictive value negative of a screening test 
$P({\overline {D}}{\overline {T}})={\frac {P({\overline {D}}{\overline {T}})P({\overline {D}})}{P({\overline {T}}{\overline {D}})P({\overline {D}})+P({\overline {T}}D)P(D)}}$ 
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
 $P({\overline {A}})$ = 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
 $P(AB)$ =a conditional statement; the probability of an event A occurring given that an event B has already occurred
 $T$ =test results

Example
