Quantitative Analysis for Management, 13/e

Key Equations

1. (2-1) $0\le P\left(\text{event}\right)\le 1$

   A basic statement of probability.

2. (2-2) $P\left(A\text{ or }B\right)=P\left(A\right)+P\left(B\right)-P\left(A\text{ and }B\right)$

   Probability of the union of two events.

3. (2-3) $P\left(A|B\right)=\frac{P\left(AB\right)}{P\left(B\right)}$

   Conditional probability.

4. (2-4) $P\left(AB\right)=P\left(A|B\right)P\left(B\right)$

   Probability of the intersection of two events.

5. (2-5) $P\left(A|B\right)=\frac{P\left(B|A\right)P\left(A\right)}{P\left(B|A\right)P\left(A\right)+P\left(B|A\prime \right)P\left(A\prime \right)}$

   Bayes’ Theorem in general form.

6. (2-6) $E\left(X\right)={\displaystyle \sum _{i=1}^n}{X}_{i}P\left(X_i\right)$

   An equation that computes the expected value (mean) of a discrete probability distribution.

7. (2-7) ${\sigma }^2=\text{Variance}={\displaystyle \sum _{i=1}^n}{\left[X_i-E\left(X\right)\right]}^{2}P\left(X_i\right)$

   An equation that computes the variance of a discrete probability distribution.

8. (2-8) $\sigma =\sqrt{\text{Variance}}=\sqrt{{\sigma }^2}$

   An equation that computes the standard deviation from the variance.

9. (2-9) Probability of r successes in n trials

   $=\frac{n!}{r!\left(n-r\right)!}{p}^r{q}^{n-r}$

   A formula ...