Question: \(\mathrm{P}(\mathrm{A})=0.68, \mathrm{P}(\mathrm{B} \mid \mathrm{A})=0.30\) , and \(\mathrm{P}(\mathrm{B} \mid \overline{\mathrm{A}})=0.02 .\) Find \(\mathrm{P}(\overline{\mathrm{A}}), \mathrm{P}(\mathrm{A}\) and \(\mathrm{B})\), and \(\mathrm{P}(\overline{\mathrm{A}}\) and B). Use these to construct a probability table. Now use the table to find the following:

\[\mathrm{P}(\overline{\mathrm{B}} \mid \mathrm{A}), \mathrm{P}(\overline{\mathrm{B}} \mid \overline{\mathrm{A}}), \mathrm{P}(\mathrm{B}), \mathrm{P}(\overline{\mathrm{B}}), \mathrm{P}(\mathrm{A} \mid \mathrm{B}), \mathrm{P}(\overline{\mathrm{A}} \mid \mathrm{B}), \mathrm{P}(\mathrm{A} \mid \overline{\mathrm{B}}), \mathrm{P}(\overline{\mathrm{A}} \mid \overline{\mathrm{B}})\]

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