bayes exercise

book/_build/html/_sources/bayes.md

@@ -239,5 +239,41 @@ The [provided spreadsheet](https://docs.google.com/spreadsheets/d/1-edxFvawj8f6v
 3. Chance a song mentions "tractor" given that it mentions "truck."
 4. Chance a song mentions "truck" given that it mentions "tractor."
 
+```{exercise-end}
+```
+
+```{exercise-start}
+:label: troll2
+```
+
+A pilgrim, traveling home, is wandering through a strange land when a troll appears:
+
+> *Woe, to pass, you must choose of these doors three.<br>
+Each leads home with some probability. <br>
+Chances 0, 50, and 100 less ten.<br>
+Independent but the order I cannot lend.<br>
+Choose traveler, lest in exile you stay.<br>
+Take three draws before I turn thee away.*
+
+1. If the first draw does not lead home, what is the probability the pilgrim opened the door that leads home with chance 0\%? 
+2. If the first draw does not lead home, what is the probability the pilgrim opened the door that leads home with chance 50\%? 
+3. If the first draw does not lead home, what is the probability the pilgrim opened the door that leads home with chance 90\%?
+
+4. If the first draw does not lead home, should the pilgrim open a different door on the next draw or try the same door again? 
+
+5. The troll, now old in his years, has seen 12 million pilgrims pass through. Each has chosen a door randomly to start and then randomly chosen a different door second if the first doesn't take them home. Finish filling in the table below with the expected counts.
+
+|                   | Door 0 second | Door 50 second | Door 90 second   |  Home after first |
+|-------------------|---------------|----------------|------------------|-------------------|
+| Door 0 first      | 0 million     |                |                  | 0 million         |
+| Door 50 first     |               | 0 million      |                  | 2 million         |
+| Door 90 first     |               |                | 0 million        | 3.6 million       |
+
+
+6. If the second draw does not lead home, should the pilgrim open a different door on the next draw? 
+7. What is the probability that the pilgrim remains in exile? 
+8. The pilgrim, alarmed by the risk of remaining in exile, bargains with the troll to replace the 0\% and 90\% chance doors with two 45\% chance doors. Is this wise? 
+9. The pilgrim, alarmed by the risk of remaining in exile, bargains with the troll to replace the 0\% and 90\% chance doors with two 80\% chance doors. Is this wise? 
+
 ```{exercise-end}
 ```

book/_build/html/bayes.html

@@ -649,6 +649,64 @@ <h2>Exercises<a class="headerlink" href="#exercises" title="Permalink to this he
 </ol>
 </section>
 </div>
+<div class="exercise admonition" id="troll2">
+
+<p class="admonition-title"><span class="caption-number">Exercise 38 </span></p>
+<section id="exercise-content">
+<p>A pilgrim, traveling home, is wandering through a strange land when a troll appears:</p>
+<blockquote>
+<div><p><em>Woe, to pass, you must choose of these doors three.<br>
+Each leads home with some probability. <br>
+Chances 0, 50, and 100 less ten.<br>
+Independent but the order I cannot lend.<br>
+Choose traveler, lest in exile you stay.<br>
+Take three draws before I turn thee away.</em></p>
+</div></blockquote>
+<ol class="arabic simple">
+<li><p>If the first draw does not lead home, what is the probability the pilgrim opened the door that leads home with chance 0%?</p></li>
+<li><p>If the first draw does not lead home, what is the probability the pilgrim opened the door that leads home with chance 50%?</p></li>
+<li><p>If the first draw does not lead home, what is the probability the pilgrim opened the door that leads home with chance 90%?</p></li>
+<li><p>If the first draw does not lead home, should the pilgrim open a different door on the next draw or try the same door again?</p></li>
+<li><p>The troll, now old in his years, has seen 12 million pilgrims pass through. Each has chosen a door randomly to start and then randomly chosen a different door second if the first doesn’t take them home. Finish filling in the table below with the expected counts.</p></li>
+</ol>
+<table class="table">
+<thead>
+<tr class="row-odd"><th class="head"><p></p></th>
+<th class="head"><p>Door 0 second</p></th>
+<th class="head"><p>Door 50 second</p></th>
+<th class="head"><p>Door 90 second</p></th>
+<th class="head"><p>Home after first</p></th>
+</tr>
+</thead>
+<tbody>
+<tr class="row-even"><td><p>Door 0 first</p></td>
+<td><p>0 million</p></td>
+<td><p></p></td>
+<td><p></p></td>
+<td><p>0 million</p></td>
+</tr>
+<tr class="row-odd"><td><p>Door 50 first</p></td>
+<td><p></p></td>
+<td><p>0 million</p></td>
+<td><p></p></td>
+<td><p>2 million</p></td>
+</tr>
+<tr class="row-even"><td><p>Door 90 first</p></td>
+<td><p></p></td>
+<td><p></p></td>
+<td><p>0 million</p></td>
+<td><p>3.6 million</p></td>
+</tr>
+</tbody>
+</table>
+<ol class="arabic simple" start="6">
+<li><p>If the second draw does not lead home, should the pilgrim open a different door on the next draw?</p></li>
+<li><p>What is the probability that the pilgrim remains in exile?</p></li>
+<li><p>The pilgrim, alarmed by the risk of remaining in exile, bargains with the troll to replace the 0% and 90% chance doors with two 45% chance doors. Is this wise?</p></li>
+<li><p>The pilgrim, alarmed by the risk of remaining in exile, bargains with the troll to replace the 0% and 90% chance doors with two 80% chance doors. Is this wise?</p></li>
+</ol>
+</section>
+</div>
 </section>
 </section>
 

book/bayes.md

@@ -239,5 +239,41 @@ The [provided spreadsheet](https://docs.google.com/spreadsheets/d/1-edxFvawj8f6v
 3. Chance a song mentions "tractor" given that it mentions "truck."
 4. Chance a song mentions "truck" given that it mentions "tractor."
 
+```{exercise-end}
+```
+
+```{exercise-start}
+:label: troll2
+```
+
+A pilgrim, traveling home, is wandering through a strange land when a troll appears:
+
+> *Woe, to pass, you must choose of these doors three.<br>
+Each leads home with some probability. <br>
+Chances 0, 50, and 100 less ten.<br>
+Independent but the order I cannot lend.<br>
+Choose traveler, lest in exile you stay.<br>
+Take three draws before I turn thee away.*
+
+1. If the first draw does not lead home, what is the probability the pilgrim opened the door that leads home with chance 0\%? 
+2. If the first draw does not lead home, what is the probability the pilgrim opened the door that leads home with chance 50\%? 
+3. If the first draw does not lead home, what is the probability the pilgrim opened the door that leads home with chance 90\%?
+
+4. If the first draw does not lead home, should the pilgrim open a different door on the next draw or try the same door again? 
+
+5. The troll, now old in his years, has seen 12 million pilgrims pass through. Each has chosen a door randomly to start and then randomly chosen a different door second if the first doesn't take them home. Finish filling in the table below with the expected counts.
+
+|                   | Door 0 second | Door 50 second | Door 90 second   |  Home after first |
+|-------------------|---------------|----------------|------------------|-------------------|
+| Door 0 first      | 0 million     |                |                  | 0 million         |
+| Door 50 first     |               | 0 million      |                  | 2 million         |
+| Door 90 first     |               |                | 0 million        | 3.6 million       |
+
+
+6. If the second draw does not lead home, should the pilgrim open a different door on the next draw? 
+7. What is the probability that the pilgrim remains in exile? 
+8. The pilgrim, alarmed by the risk of remaining in exile, bargains with the troll to replace the 0\% and 90\% chance doors with two 45\% chance doors. Is this wise? 
+9. The pilgrim, alarmed by the risk of remaining in exile, bargains with the troll to replace the 0\% and 90\% chance doors with two 80\% chance doors. Is this wise? 
+
 ```{exercise-end}
 ```