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Probability Theory: Independent and Mutually Exclusive Events - Prof. Alan Holt Kvanli, Study notes of Humanities

University of North Texas (UNT)Humanities
Prof. Alan Holt Kvanli

The concepts of independent and mutually exclusive events in probability theory. It provides formulas for calculating the probabilities of multiple independent events occurring and the probabilities of mutually exclusive events not occurring together. The document also includes examples using a community's morning and evening paper subscriptions and a poisson random variable.

Typology: Study notes

2010/2011

Uploaded on 04/15/2011

masti13
masti13 🇺🇸

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•P(A and B) = P(A) · P(B)
provided A and B are independent
•This means that events A and B don’t affect
each other
•This also applies to more than two events
•P(A and B and C) = P(A) · P(B) · P(C)
provided these three events are independent
•P(A or B) = P(A) + P(B)
provided A and B are mutually exclusive
•This means that events A and B cannot both occur
•This also applies to more than two events
•P(A or B or C) = P(A) + P(B) + P(C)
provided these three events are mutually exclusive
•This example is in the textbook
•A certain community has a morning paper and an evening paper
•The three pieces of information:
• 20% of the people take the morning paper
P(M) = .2
• 30% of the people take the evening paper
P(E) = .3
• 10% of the people take both
P(M and E) = .1
pf3

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  • P(A and B) = P(A) · P(B) provided A and B are independent
  • This means that events A and B don’t affect each other
  • This also applies to more than two events
  • P(A and B and C) = P(A) · P(B) · P(C) provided these three events are independent
  • P(A or B) = P(A) + P(B) provided A and B are mutually exclusive
  • This means that events A and B cannot both occur
  • This also applies to more than two events
  • P(A or B or C) = P(A) + P(B) + P(C) provided these three events are mutually exclusive
  • This example is in the textbook
  • A certain community has a morning paper and an evening paper
  • The three pieces of information:
  • 20% of the people take the morning paper P(M) =.
  • 30% of the people take the evening paper P(E) =.
  • 10% of the people take both P(M and E) =.

P(M or E) is 40/100 =. So, 40% of the people take one paper or the other This is a conditional probability: P(E|M) is 10/20 =. So, 50% of the morning subscribers take the evening paper probability mass function: P(X = x) is

3 −| 4 − x |

The PMF here: P(X = x) is 2 Cx(½)^2

  • “no more than” means ≤( sum of values ≤)
  • “at least” means ≥ (-1) 6 H’s in 10 flips of a coin is 10 C 6 (½)^10 = (210)(½)^10 =. mean of X is ∑x·P(x) mean = μ = np variance = σ^2 = np(1 – p) standard deviation = σ =
  • For a Poisson random variable it turns out that mean = variance

√np(^1 −^ p^ )