18M.1.SL.TZ1.T_10

pestleMathematicsAASLPaper 118M· sl-4-6-combined-mutually-exclusive-conditional-independence-prob-diagramssource ↗

A group of 60 sports enthusiasts visited the PyeongChang 2018 Winter Olympic games to watch a variety of sporting events.

The most popular sports were snowboarding (S), figure skating (F) and ice hockey (H).

For this group of 60 people:

4 did not watch any of the most popular sports,
x watched all three of the most popular sports,
9 watched snowboarding only,
11 watched figure skating only,
15 watched ice hockey only,
7 watched snowboarding and figure skating,
13 watched figure skating and ice hockey,
11 watched snowboarding and ice hockey.

Find the value of x.

Markscheme / solution

$4 + 9 + 11 + 15 + x + \left( {7 - x} \right) + \left( {11 - x} \right) + \left( {13 - x} \right) = 60$ (M1)

Note: Award (M1) for equating the sum of at least seven of the entries in their Venn diagram to 60.

$\left( {x = } \right)\,\,5$ (A1)(ft) (C2)

Note: Follow through from part (a), but only if answer is positive.

[2 marks]

Examiners’ report

[N/A]