AoPS_CP Week 10: Probability with Dependent/Independent Events

lilijia Post in AOPS_Counting_Probability
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Lesson review:
Today we have finished the second half of Chapter 8: Basic Probability Techniques and Chapter 9: Think about it!

  1. Addition or Multiplication
    We add probabilities of exclusive events: P(A or B) = P(A) + P(B);
    and multiply probabilities of independent events: P(A and B) = P(A) X P(B)
  2. Independent VS Dependent Events
    Independent Events: the probability that one event occurs in no way affects the probability of the other event occurring.
    Dependent Events: the probability of one event occurring influences the likelihood of the other event.
  3. Avoid unnecessary computation:
    1) take advantage of symmetry
    2) ignore the irrelevant information
    3) consider multiple events at once instead of dealing with them separately
    4) be flexible, think out of the box!

Homework:
Page 135: Ex 8.4.1, 8.4.4, 8.5.1, 8.5.4, 8.5.6
Page 151: Ex 9.8, 9.10, 9.12, 9.14

Additional Resource:
https://www.siyavula.com/read/maths/grade-11/probability/10-probability-02

https://www.wyzant.com/resources/lessons/math/statistics_and_probability/probability/further_concepts_in_probability

https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:dependent-events-precalc/v/independent-events-1

https://www.khanacademy.org/math/ap-statistics/probability-ap/probability-multiplication-rule/v/compound-probability-of-independent-events

See you next Sunday and I look forward to exploring the geometric probability with you! Have fun!

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