9. Thirty shoppers were asked which of apples, oranges and bananas, they regularly liked to eat.
Of these 30 shoppers
2 liked all three fruits,
5 liked oranges but did not like apples or bananas,
6 liked both oranges and bananas,
17 liked apples,
10 liked bananas.
(a) Extra information from the 30 shoppers has been shown in the Venn diagram below. Complete the Venn diagram using the information given above. [3]
(b) One shopper is chosen at random. Find the probability that this shopper does not like any of the three fruits. [1]
(c) One shopper is chosen at random from those who like apples. Find the probability that this shopper does not like oranges. [2]
Mark scheme (a)
Scheme
Marks
Comments
B3
B2 for any 4 or 5 correct or B1 for any 2 or 3 correct
FT where possible for B2 or B1
NB common solution for B2 will be
Mark scheme (b)
Scheme
Marks
Comments
\(\dfrac{1}{30}\) or equivalent
B1
ISW FT ‘their 1’, which may be zero or empty
Mark scheme (c)
Scheme
Marks
Comments
\(\dfrac{7}{17}\)
B2
FT ‘their 6’ + 1 (not their 17 as this is given)
B1 for denominator of 17 or numerator of 7 or ‘their 6’ + 1, provided the fraction is < 1 or B1 for correct answer with wrong notation e.g. 7 out of 17 or 7 : 17
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