8G - Simulations in probability
Simulations are a useful and legitimate mathematical model that are regularly used by scientists and statisticians. Simulations are used to model real world scenarios where the scenario cannot be measured directly. A real world scenario may not be measurable for a number of reasons:
- It may be inaccessible; that is, the population cannot be reached to collect data on.
- It may be too dangerous to measure the population directly.
- It may be too expensive to measure undertake the survey to collect data.
Setting the scene: Why do airlines sell too many tickets?
View full lesson on ed.ted.com: click here
Have you ever sat in a doctor’s office for hours, despite having an appointment? Has a hotel turned down your reservation because it’s full? Have you been bumped off a flight that you paid for? These are all symptoms of overbooking, a practice where businesses sell or book more than their capacity. So why do they do it? Nina Klietsch explains the math behind this frustrating practice. Lesson by Nina Klietsch, animation by Anton Trofimov. |
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8G - Example 1: Simulating a random (ant) walk
An ant is sitting in the middle of a circle of radius 3 meters. Every minute, the ant pick a random direction and moves in a straight line for 1 meter. We can simulate this scenario using tessellations.
(A more sophisticated simulation of the ant walk can be found at: https://www.geogebra.org/m/EQCMQ7Py)
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8A - Example 1: Video solution
8A - Example 1: Practice
Question 1: ABC Question 2: ABC 8A - Example 1: Solutions
Question 1: ABC Question 2: ABC |
8G - Example 2: Simulating overbooking
An interesting video on the mathematics of "overbooking" can be found be clicking here.
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8G - Example 2: Video solution
8G - Example 2: Practice
8G - Example 3: Solutions
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