9/27/26, 2:24 PM BONUS Week 4 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
BONUS Week 4 Homework
Due Sep 25 at 11:59pm
Points 1
Questions 1
Available Sep 18 at 8am - Sep 28 at 11:59pm
Time Limit None
Attempt History
Attempt Time Score
LATEST Attempt 1 2 minutes 1 out of 1
Score for this quiz: 1 out of 1
Submitted Sep 18 at 10:05pm
This attempt took 2 minutes.
Correct answer
Question 1
pts
(Lesson 3.3: Making Some .) BONUS: Now suppose that we can somehow toss random darts into a
unit cube. Further, suppose that we've inscribed a sphere with radius 1/2 inside the cube. Let be the
proportion of the darts that actually fall within the sphere. Give a Monte Carlo scheme to estimate .
a.
b.
c.
d.
The probability that a dart falls inside the sphere is the volume of the sphere divided by the volume of the
unit cube, i.e., . Thus, for large , we have , so that should do the
trick. Therefore, the answer is (d).
The probability that a dart falls inside the sphere is the volume of the sphere divided by the volume of the
unit cube, i.e., . Thus, for large , we have , so that should do the
trick. Therefore, the answer is (d).
Quiz Score: 1 out of 1
https://gatech.instructure.com/courses/538298/quizzes/799041?module_item_id=6187754 1/2
BONUS Week 4 Homework
Due Sep 25 at 11:59pm
Points 1
Questions 1
Available Sep 18 at 8am - Sep 28 at 11:59pm
Time Limit None
Attempt History
Attempt Time Score
LATEST Attempt 1 2 minutes 1 out of 1
Score for this quiz: 1 out of 1
Submitted Sep 18 at 10:05pm
This attempt took 2 minutes.
Correct answer
Question 1
pts
(Lesson 3.3: Making Some .) BONUS: Now suppose that we can somehow toss random darts into a
unit cube. Further, suppose that we've inscribed a sphere with radius 1/2 inside the cube. Let be the
proportion of the darts that actually fall within the sphere. Give a Monte Carlo scheme to estimate .
a.
b.
c.
d.
The probability that a dart falls inside the sphere is the volume of the sphere divided by the volume of the
unit cube, i.e., . Thus, for large , we have , so that should do the
trick. Therefore, the answer is (d).
The probability that a dart falls inside the sphere is the volume of the sphere divided by the volume of the
unit cube, i.e., . Thus, for large , we have , so that should do the
trick. Therefore, the answer is (d).
Quiz Score: 1 out of 1
https://gatech.instructure.com/courses/538298/quizzes/799041?module_item_id=6187754 1/2
