<ol class="abc-list"><li><div class="list-item-paragraph">In a certain university, there are $110$ Co-Curricular Activities (CCAs) clustered into $4$ categories. There are $22$ Arts and Culture CCAs, $16$ Community Service CCAs, $38$ Physical Sports CCAs and $34$ Special Interest CCAs.</div><ol class="i-list"><li><div class="list-item-paragraph">Albert wishes to find out about approaches to training of the Physical Sports CCAs, so he sends a questionnaire to $22$ Physical Sports CCAs. Explain whether these $22$ Physical Sports CCAs form a sample or a population.<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Benedict wishes to investigate the level of student engagement in CCAs, but does not want to obtain the detailed information necessary from all $110$ CCAs. Explain how he should carry out his investigation, and why he should do the investigation in this way.<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Find the number of different possible samples of $16$ CCAs, with $4$ CCAs chosen from each category.<span class="inline-marks">[2]</span></div></li></ol></li><li><div class="list-item-paragraph">The probability of events $A$, $B$ and $C$ occurring are given by $\mathrm{P}\left( A \right)=\frac{8}{25}$, $\mathrm{P}\left( B \right)=\frac{61}{100}$ and $\mathrm{P}\left( C \right)=\frac{7}{20}$ respectively. It is also known that&nbsp;$\mathrm{P}\left( A\cap C \right)=\frac{11}{100}$, $\mathrm{P}\left( \left. B \right|C \right)=\frac{13}{35}$ and $\mathrm{P}\left( A\cap B\cap C \right)=\frac{7}{100}$.</div><ol class="i-list"><li><div class="list-item-paragraph">Find $\mathrm{P}\left( B\cap C \right)$.<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">If events $A$ and $B$ are independent, find $\mathrm{P}\left( A\cap B\cap C' \right)$.<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">If events $A$ and $B$ are not known to be independent, find the greatest and least possible values of $\mathrm{P}\left( A\cap B\cap C' \right)$.<span class="inline-marks">[4]</span></div></li></ol></li></ol>

In a certain university, there are $110$ Co-Curricular Activities (CCAs) clustered into $4$ categories. There are $22$ Arts and Culture CCAs, $16$ Community Service CCAs, $38$ Physical Sports CCAs and $34$ Special Interest CCAs.

The probability of events $A$, $B$ and $C$ occurring are given by $\mathrm{P}\left( A \right)=\frac{8}{25}$, $\mathrm{P}\left( B \right)=\frac{61}{100}$ and $\mathrm{P}\left( C \right)=\frac{7}{20}$ respectively. It is also known that $\mathrm{P}\left( A\cap C \right)=\frac{11}{100}$, $\mathrm{P}\left( \left. B \right|C \right)=\frac{13}{35}$ and $\mathrm{P}\left( A\cap B\cap C \right)=\frac{7}{100}$.

2024 CJC P2 Q10

2024 CJC P2 Q10

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