openfreebooks-bookgenerator/content/math/basic-probability/core.html

<div class="book-prose">
  <p>
    Probability measures how likely an event is, from 0 (impossible) to 1 (certain).
  </p>

  <h2 id="fundamentals" class="book-prose__heading">Fundamentals</h2>
  <p class="book-formula">\[
    P(E)=\frac{\text{number of favorable outcomes}}{\text{number of equally likely outcomes}}.
  \]</p>
  <p>
    Also: \(0\le P(E)\le1\).
  </p>

  <h2 id="complement" class="book-prose__heading">Complement rule</h2>
  <p class="book-formula">\[
    P(E')=1-P(E).
  \]</p>

  <h2 id="multiple-events" class="book-prose__heading">Combined events</h2>
  <ul>
    <li>\(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)</li>
    <li>If independent: \(P(A\cap B)=P(A)P(B)\)</li>
  </ul>

  <h2 id="experimental" class="book-prose__heading">Experimental probability</h2>
  <p class="book-formula">\[
    P(E)\approx\frac{\text{observed frequency}}{\text{number of trials}}.
  \]</p>

  <h2 id="sample-space" class="book-prose__heading">Sample spaces and trees</h2>
  <p>
    Use sample-space tables or tree diagrams for multi-step outcomes.
    Multiply along branches, add across valid branches.
  </p>

  <h2 id="exam-strategy" class="book-prose__heading">Exam strategy</h2>
  <ul>
    <li>Define event clearly before calculating.</li>
    <li>Use fractions first; round at end if needed.</li>
    <li>Check complement and total probability sanity.</li>
    <li>Use diagrams to avoid missing outcomes.</li>
  </ul>
</div>