91Ó°ÊÓ

If \(P(E)=.3\), and \(P(F)=.3\), and \(E\) and \(F\) are mutually exclusive, find \(P(E \mid F)\).

If \(P(E)=.6\) and \(P(E\) and \(F)=.24\), find \(P(F \mid E)\)

If \(P(E\) and \(F)=.04\) and \(P(E \mid F)=.1,\) find \(P(F)\)

Consider a family of three children. Find the following probabilities. \(P\) (two boys | first born is a boy)

Consider a family of three children. Find the following probabilities. \(P\) (all girls | at least one girl is born)

Consider a family of three children. Find the following probabilities. \(P\) (children of both sexes \(\mid\) first born is a boy)

The distribution of the number of fiction and non-fiction books checked out at a city's main library and at a smaller branch on a given day is as follows. $$ \begin{array}{|l|l|l|l|} \hline & \text { MAIN }(\mathrm{M}) & \text { BRANCH(B) } & \text { TOTAL } \\\ \hline \text { FICTION }(\mathrm{F}) & 300 & 100 & 400 \\ \hline \text { NON-FICTION }(\mathrm{N}) & 150 & 50 & 200 \\ \hline \text { TOTALS } & 450 & 150 & 600 \\ \hline \end{array} $$ Use this table to determine the following probabilities: \(P(F)\)

The distribution of the number of fiction and non-fiction books checked out at a city's main library and at a smaller branch on a given day is as follows. $$ \begin{array}{|l|l|l|l|} \hline & \text { MAIN }(\mathrm{M}) & \text { BRANCH(B) } & \text { TOTAL } \\\ \hline \text { FICTION }(\mathrm{F}) & 300 & 100 & 400 \\ \hline \text { NON-FICTION }(\mathrm{N}) & 150 & 50 & 200 \\ \hline \text { TOTALS } & 450 & 150 & 600 \\ \hline \end{array} $$ Use this table to determine the following probabilities: \(P(M \mid F)\)

The distribution of the number of fiction and non-fiction books checked out at a city's main library and at a smaller branch on a given day is as follows. $$ \begin{array}{|l|l|l|l|} \hline & \text { MAIN }(\mathrm{M}) & \text { BRANCH(B) } & \text { TOTAL } \\\ \hline \text { FICTION }(\mathrm{F}) & 300 & 100 & 400 \\ \hline \text { NON-FICTION }(\mathrm{N}) & 150 & 50 & 200 \\ \hline \text { TOTALS } & 450 & 150 & 600 \\ \hline \end{array} $$ Use this table to determine the following probabilities: \(P(N \mid B)\)

Do the following problems involving independence. If \(P(E)=.6, P(F)=.2,\) and \(E\) and \(F\) are independent, find \(P(E\) and \(F)\)