\relax 
\@writefile{toc}{\contentsline {chapter}{\numberline {4}Conditional Probability}{133}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{chp 4}{{4}{133}}
\@writefile{toc}{\contentsline {section}{\numberline {4.1}Discrete Conditional Probability}{133}}
\newlabel{sec 4.1}{{4.1}{133}}
\newlabel{exam 4.1}{{4.1}{133}}
\newlabel{exam 4.1.5}{{4.2}{133}}
\newlabel{exam 4.2}{{4.3}{134}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.1}{\ignorespaces Tree diagram.}}{135}}
\newlabel{fig 4.1}{{4.1}{135}}
\newlabel{exam 4.3}{{4.4}{135}}
\newlabel{exam 4.4}{{4.5}{135}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.2}{\ignorespaces Reverse tree diagram.}}{136}}
\newlabel{fig 4.2}{{4.2}{136}}
\newlabel{exam 4.5}{{4.6}{136}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.3}{\ignorespaces The Monty Hall problem.}}{138}}
\newlabel{fig 4.4}{{4.3}{138}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.4}{\ignorespaces Conditional probabilities for the Monty Hall problem.}}{139}}
\newlabel{fig 4.4.5}{{4.4}{139}}
\newlabel{def 4.2}{{4.1}{139}}
\newlabel{thm 4.1}{{4.1}{140}}
\newlabel{exam 4.6}{{4.7}{140}}
\newlabel{exam 4.7}{{4.8}{140}}
\newlabel{exam 4.8}{{4.9}{141}}
\newlabel{def 4.3}{{4.2}{141}}
\newlabel{exam 4.91}{{4.10}{141}}
\newlabel{exam 4.92}{{4.11}{142}}
\newlabel{def 4.4}{{4.3}{142}}
\newlabel{exam 4.93}{{4.12}{142}}
\@writefile{lot}{\contentsline {table}{\numberline {4.1}{\ignorespaces Smoking and cancer.}}{143}}
\newlabel{table 4.1}{{4.1}{143}}
\@writefile{lot}{\contentsline {table}{\numberline {4.2}{\ignorespaces Joint distribution.}}{143}}
\newlabel{table 4.2}{{4.2}{143}}
\newlabel{def 4.4.5}{{4.4}{143}}
\newlabel{exam 4.94}{{4.13}{143}}
\newlabel{def 5.5}{{4.5}{144}}
\newlabel{exam 5.6.1}{{4.14}{144}}
\newlabel{exam 5.7}{{4.15}{145}}
\newlabel{eq 4.1}{{4.1}{145}}
\@writefile{lot}{\contentsline {table}{\numberline {4.3}{\ignorespaces Diseases data.}}{146}}
\newlabel{table 4.3}{{4.3}{146}}
\newlabel{eq 4.2}{{4.2}{146}}
\newlabel{eq 4.3}{{4.3}{146}}
\newlabel{exam 4.10}{{4.16}{146}}
\@writefile{lot}{\contentsline {table}{\numberline {4.4}{\ignorespaces Posterior probabilities.}}{147}}
\newlabel{table 4.35}{{4.4}{147}}
\newlabel{exam 4.11}{{4.17}{147}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.5}{\ignorespaces Forward and reverse tree diagrams.}}{148}}
\newlabel{fig 4.5}{{4.5}{148}}
\newlabel{exer 4.1.1}{{1}{150}}
\newlabel{exer 4.1.2}{{2}{150}}
\newlabel{exer 4.1.3}{{3}{150}}
\newlabel{exer 4.1.4}{{4}{150}}
\newlabel{exer 4.1.5}{{5}{150}}
\newlabel{exer 4.1.6}{{6}{151}}
\newlabel{exer 4.1.7}{{7}{151}}
\newlabel{exer 4.1.8}{{8}{151}}
\newlabel{exer 4.1.9}{{9}{151}}
\newlabel{exer 4.1.9.5}{{10}{151}}
\newlabel{exer 4.1.9.6}{{11}{151}}
\newlabel{exer 4.1.10}{{12}{151}}
\newlabel{exer 4.1.11}{{13}{151}}
\newlabel{exer 4.1.12}{{14}{152}}
\newlabel{exer 4.1.13}{{15}{152}}
\newlabel{exer 4.1.14}{{16}{152}}
\newlabel{exer 4.1.15}{{17}{152}}
\newlabel{exer 4.1.16}{{18}{152}}
\newlabel{exer 4.1.17}{{19}{152}}
\newlabel{exer 4.1.18}{{20}{152}}
\newlabel{exer 4.1.19}{{21}{152}}
\newlabel{exer 4.1.20}{{22}{152}}
\newlabel{exer 4.1.21}{{23}{153}}
\newlabel{exer 4.1.22}{{24}{153}}
\newlabel{exer 4.1.23}{{25}{153}}
\newlabel{exer 4.1.24}{{26}{153}}
\newlabel{exer 4.1.25}{{27}{153}}
\newlabel{exer 4.1.26}{{28}{153}}
\@writefile{lot}{\contentsline {table}{\numberline {4.5}{\ignorespaces Collins case probabilities.}}{154}}
\newlabel{table 4.4}{{4.5}{154}}
\newlabel{exer 4.1.27}{{29}{154}}
\newlabel{exer 4.1.28}{{30}{154}}
\newlabel{exer 4.1.29}{{31}{154}}
\newlabel{exer 4.1.30}{{32}{154}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.6}{\ignorespaces From Woodstock to Tunbridge.}}{155}}
\newlabel{fig 4.51}{{4.6}{155}}
\newlabel{exer 4.1.31}{{33}{155}}
\newlabel{exer 5.1.4}{{34}{155}}
\newlabel{exer 5.1.5}{{35}{155}}
\@writefile{lot}{\contentsline {table}{\numberline {4.6}{\ignorespaces Joint distribution.}}{156}}
\newlabel{table 4.5}{{4.6}{156}}
\newlabel{exer 5.1.6}{{36}{156}}
\newlabel{exer 5.1.7}{{37}{156}}
\newlabel{exer 5.1.8}{{38}{156}}
\newlabel{exer 5.1.10}{{39}{156}}
\newlabel{exer 5.1.11}{{40}{156}}
\newlabel{exer 5.1.12}{{41}{156}}
\newlabel{exer 5.1.13}{{42}{157}}
\newlabel{exer 5.1.14}{{43}{157}}
\newlabel{exer 5.1.15}{{44}{157}}
\newlabel{exer 5.1.15.5}{{45}{158}}
\newlabel{exer 5.1.19}{{46}{158}}
\newlabel{exer 5.1.24.5}{{47}{158}}
\newlabel{exer 4.1.32}{{48}{158}}
\newlabel{exer 4.1.33}{{49}{159}}
\newlabel{exer 4.1.34}{{50}{159}}
\newlabel{exer 4.1.35}{{51}{159}}
\newlabel{exer 4.1.36}{{52}{159}}
\newlabel{exer 4.1.37}{{53}{159}}
\newlabel{exer 4.1.38}{{54}{160}}
\newlabel{exer 4.1.39}{{55}{160}}
\newlabel{exer 4.1.40}{{56}{160}}
\newlabel{exer 4.1.41}{{57}{161}}
\newlabel{exer 4.1.42}{{58}{161}}
\newlabel{exer 4.1.43}{{59}{161}}
\newlabel{exer 4.1.44}{{60}{161}}
\newlabel{exer 4.1.45}{{61}{161}}
\newlabel{exer 4.1.46}{{62}{161}}
\newlabel{exer 4.1.47}{{63}{161}}
\@writefile{toc}{\contentsline {section}{\numberline {4.2}Continuous Conditional Probability}{162}}
\newlabel{sec 4.2}{{4.2}{162}}
\newlabel{exam 4.12}{{4.18}{162}}
\newlabel{exam 4.13}{{4.19}{163}}
\newlabel{exam 4.14}{{4.20}{163}}
\newlabel{exam 4.15}{{4.21}{164}}
\newlabel{def 4.5}{{4.6}{165}}
\newlabel{eq 4.4}{{4.4}{165}}
\newlabel{def 4.6}{{4.7}{165}}
\newlabel{thm 4.2}{{4.2}{165}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.7}{\ignorespaces $X_1$ and $X_2$ are independent.}}{166}}
\newlabel{fig 5.15}{{4.7}{166}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.8}{\ignorespaces $X_1$ and $X_3$ are not independent.}}{167}}
\newlabel{fig 5.16}{{4.8}{167}}
\newlabel{thm 4.3}{{4.3}{167}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.9}{\ignorespaces Beta density for $\alpha = \beta = .5,1,2.$}}{168}}
\newlabel{fig 4.6}{{4.9}{168}}
\newlabel{def 5.12}{{4.8}{168}}
\newlabel{exam 4.16}{{4.23}{168}}
\newlabel{eq 4.5}{{4.5}{170}}
\newlabel{exam 4.17}{{4.24}{170}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.10}{\ignorespaces Play the best machine.}}{171}}
\newlabel{fig 4.7}{{4.10}{171}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.11}{\ignorespaces Play the winner.}}{172}}
\newlabel{fig 4.8}{{4.11}{172}}
\newlabel{exer 4.2.1}{{1}{172}}
\newlabel{exer 4.2.2}{{2}{172}}
\newlabel{exer 4.2.3}{{3}{172}}
\newlabel{exer 4.2.4}{{4}{173}}
\newlabel{exer 4.2.5}{{5}{173}}
\newlabel{exer 4.2.6}{{6}{173}}
\newlabel{exer 4.2.7}{{7}{173}}
\newlabel{exer 4.2.8}{{8}{173}}
\newlabel{exer 4.2.8.5}{{9}{174}}
\newlabel{exer 4.2.9}{{10}{174}}
\newlabel{exer 4.2.10}{{11}{174}}
\newlabel{exer 4.2.11}{{12}{174}}
\newlabel{exer 4.2.12}{{13}{175}}
\newlabel{exer 4.2.13}{{14}{175}}
\@writefile{toc}{\contentsline {section}{\numberline {4.3}Paradoxes}{175}}
\newlabel{sec 4.3}{{4.3}{175}}
\newlabel{exam 4.3.1}{{4.25}{175}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.12}{\ignorespaces Tree for Example \ref {exam 4.3.1}.}}{176}}
\newlabel{fig 4.3}{{4.12}{176}}
\newlabel{exam 4.3.2}{{4.26}{176}}
\newlabel{exam 4.3.3}{{4.27}{176}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.13}{\ignorespaces Tree for Example \ref {exam 4.3.2}.}}{177}}
\newlabel{fig 4.3.5}{{4.13}{177}}
\newlabel{exam 4.3.4}{{4.28}{178}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.14}{\ignorespaces John Finn's version of Example \ref {exam 4.3.4}.}}{179}}
\newlabel{fig 4.9}{{4.14}{179}}
\newlabel{exam 4.3.5}{{4.29}{179}}
\newlabel{eq 4.3.1}{{4.6}{180}}
\newlabel{exam 4.3.6}{{4.30}{180}}
\newlabel{exer 4.3.1}{{1}{181}}
\newlabel{exer 4.3.2}{{2}{181}}
\newlabel{exer 4.3.3}{{3}{181}}
\newlabel{exer 4.3.4}{{4}{182}}
\newlabel{exer 4.3.5}{{5}{182}}
\newlabel{exer 4.3.6}{{6}{182}}
\@setckpt{ch4}{
\setcounter{page}{183}
\setcounter{equation}{6}
\setcounter{enumi}{6}
\setcounter{enumii}{2}
\setcounter{enumiii}{0}
\setcounter{enumiv}{0}
\setcounter{footnote}{25}
\setcounter{mpfootnote}{0}
\setcounter{part}{0}
\setcounter{chapter}{4}
\setcounter{section}{3}
\setcounter{subsection}{0}
\setcounter{subsubsection}{0}
\setcounter{paragraph}{0}
\setcounter{subparagraph}{0}
\setcounter{figure}{14}
\setcounter{table}{6}
\setcounter{examp}{30}
\setcounter{defn}{8}
\setcounter{thm}{3}
\setcounter{cor}{0}
\setcounter{prop}{0}
\setcounter{lem}{0}
}