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2.3 Exercise 9

Avg difficulty 2.5

Suppose P(A)=0.5,P(AB)=P(AC)=0.3,andP(ABCc)=0.1P \left(A\right) = 0 . 5 , P \left(A B\right) = P \left(A C\right) = 0 . 3 , \text{and} P \left(A B C^{c}\right) = 0 . 1.

Determine PA(BCc)cP \left(A\left(B C^{c}\right)^{c}\right) and P(AB∪AC∪BC)P \left(A B \cup A C \cup B C\right).

Then repeat with additional data P(AcBcCc)=0.1P \left(A^{c} B^{c} C^{c}\right) = 0 . 1 and P(AcBC)=0.05P \left(A^{c} B C\right) = 0 . 05.

Pfeiffer, Applied Probability, 2.3 Problems on Minterm Analysis, exercise 9

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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.