2.2.4 Determining Probabilities Systematically

• Consider a sample space that is
  • either finite
  • or “countably infinite”
    • the latter means that outcomes can be listed in an infinite sequence,
    • so there is a first outcome, a second outcome, a third outcome, and so on-for example, the battery testing scenario of EX 2.12 test batteries.
• Let $E_1,E_2,E_3,\dots$ denote the corresponding simple events, each consisting of a single outcome.
• A sensible strategy for probability computation is:
  • First determine each simple event probability, with the requirement that $\sum P\left(E_i\right)=1$ .
  • Then the probability of any compound event $A$ is computed by adding together the $P\left(E_i\right)$ ‘s for all $E$ ‘s in $A$ :

$$P\left(A\right)=\sum _{\text{all }E;s\text{ in }A}P\left(E_i\right)$$

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EX 2.15 select car of train