Question 1
LEVEL 6
50 people are asked whether they like American football (A), Bowling (B) or Cricket (C).
All 50 people like at least 1 of the sports
10 people like all 3 sports
3 people like American football and bowling, but not cricket
16 people like bowling and cricket
17 people like American football and cricket
27 people like bowling
9 people like only American football
Part of a Venn diagram representing the above information has already been filled in.
Find the values of x and y
Select the correct answer from the list below:
A: x = 7, y = 8
B: x = 8, y = 7
C: x = 7, y = 7
D: x = 8, y = 8
CORRECT ANSWER: A
WORKED SOLUTION:
We know that 17 people like American football and cricket.
We also know that 10 people like all three sports.
Therefore, there are 17 - 10 = 7 who like American football and cricket, but not bowling.
This is the value of x, so x = 7
We know that 27 people like bowling
There are 3 people that like American football and bowling, but not cricket
There are 10 people like all 3 sports
There are 16 people like bowling and cricket, and so 16-10=6 people that like bowling and cricket, but not American football.
Therefore, there are 27 - 3 - 10 - 6 = 8 people that like only bowling.
This is the value of y, so y = 8
Question 2
LEVEL 6
There are set A and set B are displayed in the Venn diagram below.
There are 80 items in the universal set \xi.
Find the value of x.
Select the correct answer from the list below:
A: x = 9
B: x = 7
C: x = 8
D: x = 6
CORRECT ANSWER: A
WORKED SOLUTION:
(2x+6) + (4x) + (20-x) + 9 = 80
5x + 35 = 80
5x = 45
x = 9
Question 3
LEVEL 6
In the Venn diagram below, C represents students selecting Chemistry and T represents students selecting Technology.
Use the Venn diagram to find the probability that someone takes Chemistry, given that they take Technology.
Select the correct answer from the list below:
A: \dfrac{6}{28}
B: \dfrac{6}{38}
C: \dfrac{22}{28}
D: \dfrac{28}{38}
CORRECT ANSWER: A
WORKED SOLUTION:
We know that 22+6 = 28 people take Technology.
Then there are 6 out of those people who take Chemistry.
Therefore the probability is \dfrac{6}{28}
Question 4
LEVEL 6
In the Venn diagram below, A represents people that have visited Andorra and B represents people that have visited Belgium.
Use the Venn diagram to find the probability that a person chosen at random has visited Andorra, given that they have only visited exactly one of the countries.
Select the correct answer from the list below:
A: \dfrac{11}{23}
B: \dfrac{12}{23}
C: \dfrac{11}{30}
D: \dfrac{11}{33}
CORRECT ANSWER: A
WORKED SOLUTION:
There are 11+12=23 people that have visited exactly one of the countries.
Of these 23 people, 11 of them have visited Andorra.
Therefore the probability is \dfrac{11}{23}
Question 5
LEVEL 6
In the Venn diagram below, F represents people that like Fish, H represents people that like Ham, and C represents people that like Chicken.
Use the Venn diagram to find the probability that a person chosen at random likes all three foods, given that they like Fish.
Select the correct answer from the list below:
A: \dfrac{2}{12}
B: \dfrac{2}{3}
C: \dfrac{9}{12}
D: \dfrac{3}{12}
CORRECT ANSWER: A
WORKED SOLUTION:
There are 3 + 5 + 2 + 2 = 12 people that like Fish.
Of these 12 people, there are 2 people that like all three foods.
Therefore, the probability is \dfrac{2}{12}