\(B=\{\text{first 5 prime numbers}\hspace{0.15em}\}\)
Find \(n(\varepsilon)\) in terms of \(k\).[1]
Find the minimum value of \(k\).[1]
Hence, list the elements in the set \(A^{\prime}\cap B\).[2]
Set \(P\), set \(Q\) and set \(R\) are such that \(R\subset Q\) and \(R\cap P=\varnothing\).
On the Venn Diagram, draw set \(R\).[1]
Hence, shade the region which represents \((R\cup Q)^{\prime}\cap P\).[1]
In a group of 50 students, some are enrolled in the Mathematics Talent Programme only, some are enrolled in the Science Talent Programme only, some are enrolled in both programmes, while the rest are enrolled in neither programme.
One of the students from the Science Talent Programme is selected at random.
The probability that it is a student who is also in the Math Talent Programme is \(\dfrac35\).
Complete the table of information about the 50 students in the group.[2]
Science Talent Programme
Not Science Talent Programme
Math Talent Programme
15
Not Math Talent Programme
5
Three students are selected at random from the whole group.
Find the probability that at least one of them is enrolled in a Talent Programme.[2]
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Answer:(a)(i) \(k+5\) for integer \(k\). (ii) \(11\). (iii) \(\{3,5,7,11\}\). (b) \(R\subset Q\setminus P\); shade \(P\setminus Q\). (c) Missing entries: \(18,12\); probability \(\dfrac{1959}{1960}\).