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Back to 3.2 Problems on Conditional Probability

3.2 Exercise 1

Avg difficulty 2.5

Given the following data:

P ( A ) = 0 . 55 , P ( A B ) = 0 . 30 , P ( B C ) = 0 . 20 , P ( A c ∪ B C ) = 0 . 55 , P ( A c B C c ) = 0 . 15 P \left(A\right) = 0 . 55 , P \left(A B\right) = 0 . 30 , P \left(B C\right) = 0 . 20 , P \left(A^{c} \cup B C\right) = 0 . 55 , P \left(A^{c} B C^{c}\right) = 0 . 15

Determine, if possible, the conditional probability P(Ac|B)=P(AcB)/P(B)P \left(\right. A^{c} \left|\right. B \left.\right) = P \left(A^{c} B\right) / P \left(B\right).

Pfeiffer, Applied Probability, 3.2 Problems on Conditional Probability, exercise 1

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Adapted from Applied Probability © 2009 Paul E. Pfeiffer. Licensed under CC BY 3.0. Source: Applied Probability. Imported at revision d7a0420.