20 120 gardeners were asked if they grow carrots (\(C\)) or potatoes (\(P\)) or tomatoes (\(T\))
Of these gardeners
43 grow carrots 12 grow carrots and potatoes and tomatoes 18 grow carrots and potatoes 27 grow carrots and tomatoes 32 grow potatoes and tomatoes 29 do not grow carrots or potatoes or tomatoes
The number of these gardeners who grow only potatoes is equal to the number of these gardeners who grow only tomatoes.
(a) Complete the Venn diagram to show this information. (3)
(b) Find \(\mathrm{n}(T' \cap C)\) (1)
One of the gardeners who grows carrots is chosen at random.
(c) Calculate the probability that this gardener also grows potatoes. (2)
Mark scheme (a)
Scheme
Marks
B3
(3)
Notes
B3: for all numbers in correct regions (B2 for 5, 6 or 7 correct numbers B1 for 3 or 4 correct numbers)
Mark scheme (b)
Scheme
Marks
Answer: 16
B1
(1)
Notes
B1: ft for their \(a\) + their \(b\)
Do not ft if there are no values for \(a\) and \(b\)
Mark scheme (c)
Scheme
Marks
M1
\(\dfrac{18}{43}\)
A1
(2)
(6 marks)
Notes
M1: for \(\dfrac{n}{43}\) where \(n \lt 43\) or \(\dfrac{18}{m}\) where \(m \gt 18\) or
ft their \(\dfrac{b + c}{p}\) where \(p \gt b + c\) or
ft their \(\dfrac{q}{a + b + c + d}\) where \(q \lt a + b + c + d\)
Do not ft if there are no values for \(a\), \(b\), \(c\) and \(d\)
A1: oe eg 0.41(860…) or 41(.860…)% truncated or rounded or ft their \(\dfrac{b + c}{a + b + c + d}\) as a fraction or a decimal or a percentage
