# Lesson 31 — Survivability and the PK Chain

<p class="block-synopsis">Put a probability on every link of the L1 kill chain and one engagement's kill probability becomes a product, P<sub>K</sub> = P<sub>H</sub> · P<sub>K|H</sub> — susceptibility times vulnerability. Independent encounters multiply into a mission survival P<sub>S</sub> = Π(1 − P<sub>K,i</sub>), and the logarithm turns that product into a sum of risks, −ln P<sub>S</sub>, the cost a route planner can add. The Final Project is issued today.</p>

<div class="block-toc">
  <a class="bt-card bt-reading" href="L31_SurvivabilityAndPK_Reading.html">
    <span class="bt-kind">Reading</span>
    <h4>Survivability and the PK Chain</h4>
    <p>Ball's susceptibility and vulnerability, the kill chain as a product of conditional links, the two toolkits of levers, and additive risk across a route.</p>
  </a>
  <a class="bt-card bt-flashcards" href="L31_Flashcards.html">
    <span class="bt-kind">Flashcards</span>
    <h4>Review deck</h4>
    <p>Key terms and relations from the lesson, in a self-test deck.</p>
  </a>
  <a class="bt-card bt-preflight" href="L31_Preflight.html">
    <span class="bt-kind">Pre-flight</span>
    <h4>Pre-flight quiz</h4>
    <p>Five questions to work before class — anyone can be called to the board.</p>
  </a>
  <a class="bt-card bt-slides" href="../decks/L31_SurvivabilityAndPK.html" target="_blank" rel="noopener">
    <span class="bt-kind">Slides</span>
    <h4>Lesson slides</h4>
    <p>The deck we work through in class — an HTML deck you can annotate in the browser, with a print view for saving a PDF.</p>
  </a>
  <a class="bt-card bt-demo" href="../block01/L01_KillChainExplorer_Demo.html">
    <span class="bt-kind">Demo · L1 revisit</span>
    <h4>Kill Chain Explorer</h4>
    <p>The L1 demo, revisited: walk each link again and name the block that bought each lever and the probability it shrinks.</p>
  </a>
</div>
