CSEE (Form 4) Sets and Probability — practice questions

1. List $P$, the multiples of 5 below 35: $\{5,10,15,20,25,30\}$. 2. List $Q$, the odd numbers strictly between 14 and 30: $\{15,17,19,21,23,25\}$. 3. The intersection holds only members appearing in both lists. 4. Checking each element of $P$: 15 and 25 are odd and lie in range; 5 and 10 are below 14, and 20 and 30 are even. 5. So $P\cap Q=\{15,25\}$. _Source: NECTA CSEE 2022 Basic Mathematics 041, Question 3: Sets and Probability_

1. Since 10 grow neither, the union is $n(C\cup M)=50-10=40$. 2. Use $n(C\cup M)=n(C)+n(M)-n(C\cap M)$. 3. Substitute: $40=25+n(M)-16$, so $n(M)=31$. 4. That 31 is everyone growing maize, including the 16 who also grow cashew. 5. Maize only is therefore $31-16=15$. Answering 31 stops one step early and counts the overlap twice over. _Source: NECTA CSEE 2022 Basic Mathematics 041, Question 3: Sets and Probability_

1. 'At least two' covers exactly two germinating and all three germinating. 2. Exactly three: $\left(\tfrac13\right)^3=\tfrac1{27}$. 3. Exactly two: choose which two in 3 ways, giving $3\times\left(\tfrac13\right)^2\times\tfrac23=\tfrac6{27}$. 4. The two cases are mutually exclusive, so add them. 5. Total $=\tfrac6{27}+\tfrac1{27}=\tfrac7{27}$. Stopping at $\tfrac6{27}$ forgets the all-three branch of the tree diagram. _Source: NECTA CSEE 2022 Basic Mathematics 041, Question 3: Sets and Probability_