Mathematics 4024 · O Level · Sets

Sets — practice question

Let the sets be defined as follows: $\mathcal{E} = \{x : x \text{ is an integer } 10 \leq x \leq 40\}$ $P = \{x : x \text{ is a multiple of } 6\}$ $Q = \{x : x \text{ is a square number}\}$
(a(i))[1]

State the elements of $P \cup Q$.

(a(ii))[1]

Calculate $n(P' \cap Q)$.

(b)[1]

Describe the shaded region in the Venn diagram using set notation.

(c(i))[2]

Every student who studies both Arabic and Spanish also studies French. $7$ students study French only. $8$ students study Arabic. Use this information to complete the Venn diagram.

(c(ii))[2]

Select two of the $25$ students at random. Find the probability that both study Spanish only.

(c(iii))[3]

Choose three of the students at random from those who study French. Find the probability that exactly one of them also studies Arabic.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: The set is $\{12,16,18,24,25,30,36\}$.

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