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1.4 Exercise 14

Avg difficulty 2.5

For each of the following probability “assignments”, fill out the table. Which assignments are not permissible? Explain why, in each case.

$P \left(A\right)$	$P \left(B\right)$	$P \left(A B\right)$	$P \left(A \cup B\right)$	$P \left(A B^{c}\right)$	$P \left(A^{c} B\right)$	$P \left(A\right) + P \left(B\right)$
0.3	0.7	0.4
0.2	0.1	0.4
0.3	0.7	0.2
0.3	0.5	0
0.3	0.8	0

Pfeiffer, Applied Probability, 1.4 Problems on Probability Systems, exercise 14

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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.