7. A group of 20 people visited Anglesey for a weekend break.
10 of the group visited Beaumaris Castle.
13 of the group visited South Stack Lighthouse.
4 of the group did not visit either of these places.
(a) Complete the Venn diagram below to show this information. The universal set, ε, contains all of the 20 people in the group. [3]
(b) One person is chosen at random from the group. What is the probability that this person visited only one of the two places? [2]
Mark scheme (a)
Scheme
Marks
Comments
Any ‘blank space’ to be taken as 0.
B1
For the 4 in correct position.
B1
For the 7 in correct position.
B1
For the 3 AND 6 in correct positions. OR two of the following conditions met (i) 10 − ‘their (non-zero) 7’ (ii) 13 – ‘their (non-zero) 7’. (iii) total of four numbers = 20. SC1 for all regions correct but using alternative notation e.g. tallies.
Mark scheme (b)
Scheme
Marks
Comments
9/20 or equivalent. ISW
B2
B1 for a numerator of 9 (F.T. ‘their 3’ + ‘their 6’) in a fraction < 1. B1 for a denominator of 20 in a fraction < 1.
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