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+Each leads home with some probability.
+Chances 0, 50, and 100 less ten.
+Independent but the order I cannot lend.
+Choose traveler, lest in exile you stay.
+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} ``` \ No newline at end of file diff --git a/book/_build/html/bayes.html b/book/_build/html/bayes.html index 9cb5926..3e73fbc 100644 --- a/book/_build/html/bayes.html +++ b/book/_build/html/bayes.html @@ -649,6 +649,64 @@

Exercises + +

Exercise 38

+
+

A pilgrim, traveling home, is wandering through a strange land when a troll appears:

+
+

Woe, to pass, you must choose of these doors three.
+Each leads home with some probability.
+Chances 0, 50, and 100 less ten.
+Independent but the order I cannot lend.
+Choose traveler, lest in exile you stay.
+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. +
  3. If the first draw does not lead home, what is the probability the pilgrim opened the door that leads home with chance 50%?

  4. +
  5. If the first draw does not lead home, what is the probability the pilgrim opened the door that leads home with chance 90%?

  6. +
  7. 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?

  8. +
  9. 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.

  10. +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

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

+
    +
  1. If the second draw does not lead home, should the pilgrim open a different door on the next draw?

  2. +
  3. What is the probability that the pilgrim remains in exile?

  4. +
  5. 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?

  6. +
  7. 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?

  8. +
+
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+Each leads home with some probability.
+Chances 0, 50, and 100 less ten.
+Independent but the order I cannot lend.
+Choose traveler, lest in exile you stay.
+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} ``` \ No newline at end of file