AoPS_CP Week 11: Geometric Probability

lilijia Post in AOPS_Counting_Probability，
25 November 2019
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Lesson Review:

Geometric Probability can be used in situations where we don’t have a set of individual items to count; rather, we have infinitely many outcomes which can be nicely represented using some geometric object (a line segment, a region of a plane, etc). Or say, we use geometric probability when our outcomes are continuous rather than discrete.

We learned probability using lengths and areas. (In the future, you may meet some problems that require volumes.)

P (success) = Size of successful region/size of possible region

There are 3 types of geometric probabilities, one for each of the commonly used dimensions of space; length, area and volume. Target length. 1D. P(Target) = Total length. Target area. 2D. P(Target) = Total area. Target volume. 3D. P(Target) = Total volume.

Homework:

  • P156 Ex. 10.2.1, 10.2.3, 10.2.5
  • P161 Ex 10.3.1-10.3.4
  • Bonus: P162 Ex 10.7, P163 Ex 10.16

Other Resources:

https://www.khanacademy.org/math/ap-statistics/random-variables-ap/geometric-random-variable/e/geometric-probability

*Next Sunday we have no school. Wish everyone a great Thanksgiving holiday! See you on 12/08!

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