Chapter 5 Formulas and Vocabulary

• Classical method of assigning probabilities (p. 244).

  $P\left(E\right)={\displaystyle \frac{\text{number}\hspace{0.17em}\text{of}\hspace{0.17em}\text{outcomes}\hspace{0.17em}\text{in}\hspace{0.17em}E}{\text{number}\hspace{0.17em}\text{of}\hspace{0.17em}\text{outcomes}\hspace{0.17em}\text{in}\hspace{0.17em}\text{sample}\hspace{0.17em}\text{space}}}={\displaystyle \frac{N\left(E\right)}{N\left(S\right)}}$

• Event (p. 241)
• Experiment (p. 241)
• Law of Large Numbers (p. 249)
• Law of Total Probability (p. 241)
• Outcome (p. 241)
• Probability (p. 240)
• Probability model (p. 241)

• Relative frequency method of assigning probabilities (also known as the empirical method) (p. 249).

  $P\left(E\right)\approx {\displaystyle \frac{\text{frequency}\hspace{0.17em}\text{of}\hspace{0.17em}E}{\text{number}\hspace{0.17em}\text{of}\hspace{0.17em}\text{trials}\hspace{0.17em}\text{of}\hspace{0.17em}\text{experiment}}}$

• Sample space (p. 241)
• Simulation (p. 248)
• Subjective probability (p. 252)
• Tree diagram (p. 245)

• Addition Rule (p. 262).

  $P\left(A\hspace{0.17em}\text{or}\hspace{0.17em}B\right)=P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)$

• Addition Rule for Mutually Exclusive Events (p. 264). If $A$ and $B$ are mutually exclusive, then $P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)$.
• Complement of an event A (p. 259). Denoted as $A^C$.
• Intersection of two events A and B (p. 261). Denoted as $A\cap B\hspace{0.17em}\text{or}\hspace{0.17em}\text{as}\hspace{0.17em}“A\hspace{0.17em}\text{and}\hspace{0.17em}B.”$
• Mutually exclusive (disjoint) events (p. 263)

• Probabilities for complements (p. 260).

  $P\left(A\right)+P\left(A^C\right)=1,P\left(A\right)=1-P\left(A^C\right),\hspace{0.17em}\text{and}\hspace{0.17em}P\left(A^C\right)=1-P\left(A\right)$

• Union of two events $A$ and $B$ (p. 261). Denoted as $A\cup B\hspace{0.17em}\text{or}\hspace{0.17em}\text{as}\hspace{0.17em}“A\hspace{0.17em}\text{or}\hspace{0.17em}B.”$

• Conditional probability (p. 271).

  $P\left(B|A\right)={\displaystyle \frac{P\left(A\cap B\right)}{P\left(A\right)}}={\displaystyle \frac{N\left(A\cap B\right)}{N\left(A\right)}}$

• Independent events (p. 274). Events $A$ and $B$ are independent if $P\left(A|B\right)=P\left(A\right)\hspace{0.17em}\text{or}\hspace{0.17em}\text{if}\hspace{0.17em}P\left(B|A\right)=P\left(B\right)$.
• Multiplication Rule (p. 276). $P\left(A\cap B\right)=P\left(B\right)P\left(A|B\right)$ or, equivalently, $P\left(A\cap B\right)=P\left(A\right)P\left(B|A\right)$.
• Multiplication Rule for Independent Events (p. 277). If events $A$ and $B$ are independent, then $P\left(A\cap B\right)=P\left(A\right)P\left(B\right)$
• Multiplication Rule for n Independent Events (p. 280). If $A$, $B$, $C$, ... are independent events, then $P\left(A\cap B\cap C\cap \dots \right)=P\left(A\right)P\left(B\right)P\left(C\right)\dots$.
• Sampling with replacement (p. 277)
• Sampling without replacement (p. 277)

• Acceptance sampling (p. 300)

• Combination (p. 296).

  ${\hspace{0.17em}}_n{C}_r={\displaystyle \frac{n!}{r!\left(n-r\right)!}}$

• Factorial symbol n! (p. 294). $0!=1;1!=1;n!=n\left(n-1\right)\left(n-2\right)\dots 3·2·1$
• Multiplication Rule for Counting (p. 293)

• Permutation (p. 295).

  ${\hspace{0.17em}}_n{P}_r={\displaystyle \frac{n!}{\left(n-1\right)!}}$

• Permutations of nondistinct items (p. 299).

  ${\hspace{0.17em}}_n{P}_r={\displaystyle \frac{n!}{n_1!\hspace{0.17em}·n_2!\hspace{0.17em}·\dots ·\hspace{0.17em}{n}_k!}}$