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.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The answer is $5$.” …