Question: Suppose that \(\mathrm{P}(\mathrm{A})=.75, \mathrm{P}(\mathrm{B})=.40\), and \(\mathrm{P}(\mathrm{A} \cap \mathrm{B})=.25 \quad\) Calculate each of the following:

1. \(\mathrm{P}(\mathrm{A} \cup \mathrm{B})\)
2. \(\mathrm{P}(\mathrm{A} \mid \mathrm{B})\)
3. \(\mathrm{P}(\mathrm{B} \mid \mathrm{A})\)
4. \(\mathrm{P}(\overline{\mathrm{A}} \cup \mathrm{B})\)
5. \(\mathrm{P}(\mathrm{A} \mid \overline{\mathrm{B}})\)
6. \(\mathrm{P}(\overline{\mathrm{A}} \mid \mathrm{B})\)
7. Are A and B independent events? Why or why not?
8. Are A and B mutually exclusive events? Why or why not?

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