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Probability Basicshard
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Let AAA and BBB be independent events with P(A)=0.4P(A) = 0.4P(A)=0.4 and P(B)=0.5P(B) = 0.5P(B)=0.5. A third event CCC has the following conditional probabilities:

  • P(C∣A∩B)=0.6P(C \mid A \cap B) = 0.6P(C∣A∩B)=0.6
  • P(C∣Ac∩B)=0.2P(C \mid A^c \cap B) = 0.2P(C∣Ac∩B)=0.2
  • P(C∣A∩Bc)=0.3P(C \mid A \cap B^c) = 0.3P(C∣A∩Bc)=0.3
  • P(C∣Ac∩Bc)=0.1P(C \mid A^c \cap B^c) = 0.1P(C∣Ac∩Bc)=0.1 Determine the conditional probability P(A∩B∣C)P(A \cap B \mid C)P(A∩B∣C).