Simple Probability Diagrams Practice Questions

80 members of a sports club were each asked which one sport they play most often.

The two-way table shows some information about their answers.

	Tennis	Badminton	Squash	Total
Female	14		9	38
Male	13
Total		25		80

$E = \{\text{whole numbers from 1 to 15}\}$

$A = \{\text{multiples of }3\}$

$B = \{\text{factors of }30\}$

80 people applied for a job at a garden centre.

45 of the applicants were women.

18 of the women were invited to an interview.

Altogether, 37 of the 80 applicants were invited to an interview.

150 people were asked how they usually travel to work and how old they are.

• 84 of the people are under 30 years old.
• 62 of the people travel by car.
• 25 of the people who travel by car are under 30 years old.
• 38 of the people walk.
• 20 of the people who walk are 30 years old or over.
• The rest of the people travel by bus.

	Bus	Car	Walk	Total
Under 30
30 or over
Total

240 students took part in a maths challenge.

135 of the students were in Year 10.

$\frac{5}{9}$ of the Year 10 students were awarded a certificate.

Altogether, 128 of the 240 students were awarded a certificate.

50 people were asked which of the countries France, Germany and Italy they have visited.

Of these people:

• 5 have visited all three countries
• 12 have visited France and Germany
• 9 have visited Germany and Italy
• 10 have visited France and Italy
• 28 have visited France
• 25 have visited Germany
• 21 have visited Italy

$F$ is the set of people who have visited France.
$G$ is the set of people who have visited Germany.
$I$ is the set of people who have visited Italy.

A music club has 60 members. Each member was asked whether they play the piano, the guitar or the violin.

Of the 60 members:

• 34 play the piano
• 11 play the piano and the guitar
• 4 play all three instruments
• 9 play the violin
• 3 play the guitar and the violin but not the piano
• every member who plays the violin plays at least one other instrument
• 7 play none of these three instruments

$P$ is the set of members who play the piano.
$G$ is the set of members who play the guitar.
$V$ is the set of members who play the violin.

All of the students at a college took a first aid test.

$\frac{3}{5}$ of the students were girls.

$\frac{3}{4}$ of the girls passed the test.

$\frac{5}{8}$ of the boys passed the test.

In total, 168 students passed the test.