Mathematics

Problem

11. A fair die is rolled. Consider events

\mathrm{E}=\{1,3,5\}, \mathrm{F}=\{2,3\}

and

\mathrm{G}=\{2,3,4,5\}

Find (i)

\mathrm{P}(\mathrm{E} \mid \mathrm{F})

and

\mathrm{P}(\mathrm{F} \mid \mathrm{E})

(ii)

\mathrm{P}(\mathrm{E} \mid \mathrm{G})

and

\mathrm{P}(\mathrm{G} \mid \mathrm{E})

(iii)

\mathrm{P}((\mathrm{E} \cup \mathrm{F}) \mid \mathrm{G})

and

\mathrm{P}((\mathrm{E} \cap \mathrm{F}) \mid \mathrm{G})