Data Science Classroom Series – 01/Dec/2021

Probability of a Union of Events

  • We also know that for a set of disjoin events A(i)
  • For every two events
P(A U B) = P(A) + P (B) - P(A ∩ B)
  • This can be extended to 3 or More events
P(A U B U C) = P(A) + P(B) + P(C) - {P (A ∩ B) + P(B ∩ C) + P(A ∩ C)} + P(A ∩ B ∩ C)
  • Example: Consider 200 students
  • 50 students take programming (P)
  • 100 Students take electronics (E)
  • 75 Students take Maths (M)
  • 30 students take programming+Electronics
  • 45 students take electronics+maths
  • 25 students take electornics+programming
  • 15 students take all the three classes
  • Some students take no classes from the list
  • What is the probability that a student takes atleast one class

Conditional Probability

  • Lets assume you play outdoor sports, you care about rain
  • Compare
  • Probability it will rain today (Unconditional Probability)
  • Probability it will rain today give its been raining for last two days (Conditional Probability)
  • The conditional probability of event A given event B has occured is
  • Example-1:
  • The unconditional probability that you will roll 3 on a balanced die roll => 1/6
  • But what if you observed an odd number
  • This reduces number of options => {1,3,5} => conditional probability => 1/3
  • Lets use the formula
  • Scenario: We have gone to food plaza. Our friend Arundhati has placed a bet of 100 rs saying next person we meet will love both biryani and pizza
  • We have collected some data and represented in colorful venn diagram
  • So if we represent in contingency table, They contain the same information
  • unconditional probabilities:
  • Row total & Column Total
  • What is probability of not loving biryani given he loves pizza => 5/7

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