Update curriculum content and improve site metadata: Change the status of multiple math chapters from 'planned' to 'live' in the JSON curriculum file. Enhance the chapter content in spec.md with updated best practices for chapter creation. Revise the feed and sitemap XML files to include new chapters and their last modified timestamps for better SEO and navigation. Update the section title in the why-sections template for clarity.

content/math/basic-probability/core.html

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+<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>