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1.4 Exercise 13

Avg difficulty 2.5

Suppose P(A)=0.5P \left(A\right) = 0 . 5 and P(B)=0.3P \left(B\right) = 0 . 3. What is the largest possible value of P(AB)P \left(A B\right)? Using the maximum value of P(AB)P \left(A B\right), determine P(ABc)P \left(A B^{c}\right), P(AcB)P \left(A^{c} B\right), P(AcBc)P \left(A^{c} B^{c}\right) and P(A∪B)P \left(A \cup B\right). Are these values determined uniquely?

Pfeiffer, Applied Probability, 1.4 Problems on Probability Systems, exercise 13

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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.