In this year, each of the 40 students has travelled by at least one of plane ($P$), train ($T$) or boat ($B$). 7 travelled by plane only. 11 travelled by train only. 9 travelled by boat only. $n(P \cap T) = 8$, $n(B \cap T) = 3$, $n(B \cap P) = 6$.
(a)[3]
Complete the Venn diagram.
(b)[1]
Find the value of $n((P \cup B)')$.
(c)[1]
Use set notation to finish the statement $(P \cup T \cup B)' =$
(d)[2]
Calculate the probability that both of them have travelled only by plane.
(e)[2]
Calculate the probability that they have both also travelled by plane.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “A Venn diagram completed correctly” …