Mathematics 0580 · IGCSE · Sets

Sets — practice question

30 students were surveyed about whether they owned a bicycle (B), a mobile phone (M) and a computer (C). Their responses are displayed in the Venn diagram. The diagram gives these counts: In B only: 2; B∩M: 4; M only: x; B∩C: 1; B∩M∩C: 7; M∩C: 6; C only: 3; outside all sets: 2.
(a)[1]

Calculate the value of $x$.

(b)[1]

Use set notation to describe the shaded part of the Venn diagram.

(c)[1]

Find $n(C \cap (M \cup B)')$.

(d(i))[1]

Write down the probability that the selected student belongs to the set $M'$.

(d(ii))[1]

Write down the probability that the selected student has a bicycle.

(e)[3]

Find the probability that each of these students has a mobile phone but no bicycle.

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