🎯As the bullseye shrinks with each hit, the game becomes progressively harder.
📏The size of the bullseye after each hit is determined by the distance of the shot from the center.
🔢The expected score can be calculated by taking the sum of the probabilities of hitting each score.
🔅The probability of hitting the bullseye with each shot decreases as the bullseye shrinks.
🔺The volume of a 4-dimensional sphere is pi squared halves, while the volume of a 4-dimensional cube is 16.
What happens when you hit the bullseye?
—When you hit the bullseye, the bullseye shrinks in size, making it harder to hit with each subsequent shot.
How is the size of the bullseye determined?
—The size of the bullseye after each shot is determined by the distance of the shot from the center.
How is the expected score calculated?
—The expected score is calculated by taking the sum of the probabilities of hitting each score.
Does the probability of hitting the bullseye decrease with each shot?
—Yes, as the bullseye shrinks with each hit, the probability of hitting it decreases.
What is the volume of a 4-dimensional sphere and cube?
—The volume of a 4-dimensional sphere is pi squared halves, while the volume of a 4-dimensional cube is 16.
00:00Introduction to the game of darts and the concept of shrinking bullseye.
02:20Explanation of the game rules and how the bullseye shrinks with each hit.
05:30Calculation of the expected score and probabilities of hitting different scores.
08:30Analysis of the probability of hitting the bullseye with each shot.
12:30Comparison of the volumes of a 4-dimensional sphere and cube.
