Draw a Venn diagram to represent the given information, using sets labelled $B$, $C$ and $H$.

Show that $x = 3$.

Write down the value of $n(B \cap C)$.

Find the probability that this person

(i)     went on at most one trip;

(ii)     went on the coach trip, given that this person also went on both the helicopter trip and the boat trip.

     (A5)

Notes:     Award (A1) for rectangle and three labelled intersecting circles (U need not be seen),

(A1) for 3 in the correct region,

(A1) for 8 in the correct region,

(A1) for 5, 13 and 16 in the correct regions,

(A1) for $x$, $2x$ and $4x$ in the correct regions.

[5 marks]

$8 + 13 + 16 + 3 + 5 + x + 2x + 4x = 66$    (M1)

Note:     Award (M1) for either a completely correct equation or adding all the terms from their diagram in part (a) and equating to 66.

Award (M0)(A0) if their equation has no $x$.

$7x = 66 - 45$ OR $7x + 45 = 66$     (A1)

Note:     Award (A1) for adding their like terms correctly, but only when the solution to their equation is equal to 3 and is consistent with their original equation.

$x = 3$    (AG)

Note:     The conclusion $x = 3$ must be seen for the (A1) to be awarded.

[2 marks]

15     (A1)(ft)

Note:     Follow through from part (a). The answer must be an integer.

[1 mark]

(i)     $\frac{{42}}{{66}}{\text{ }}\left( {\frac{7}{{11}},{\text{ }}0.636,{\text{ }}63.6\% } \right)$     (A1)(ft)(A1)(G2)

Note:     Award (A1)(ft) for numerator, (A1) for denominator. Follow through from their Venn diagram.

(ii)     $\frac{3}{9}{\text{ }}\left( {\frac{1}{3},{\text{ }}0.333,{\text{ }}33.3\% } \right)$     (A1)(A1)(ft)(G2)

Note:     Award (A1) for numerator, (A1)(ft) for denominator. Follow through from their Venn diagram.

[4 marks]