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Probability · Paper 1 — Free Maths AI HL Practice Questions

1FoundationSAQ-SBasic probability concepts and rules5 marksPaper 1~8 min

A bag contains 7 red marbles and 3 blue marbles. A marble is selected at random, its colour is noted, and it is not replaced. A second marble is then selected at random.

(a)

Find the probability that both marbles are the same colour. [3 marks]

(b)

Given that both marbles are the same colour, find the probability that both are red. [2 marks]

Solutions

2MasterySAQ-SBasic probability concepts and rules5 marksPaper 1~8 min

In a school,

60\%

of students play football and

45\%

play basketball. It is known that

25\%

of students play both sports.

(a)

Show that the probability that a randomly selected student plays at least one of these two sports is

0.80

. [2 marks]

(b)

Find the probability that a randomly selected student plays exactly one of these two sports. [1 mark]

(c)

Given that a randomly selected student plays at least one of these two sports, find the probability that they play both sports. [2 marks]

Solutions

3ChallengeSAQ-LBasic probability concepts and rules10 marksPaper 1~15 min

A university offers three languages: French (

F

), German (

G

), and Spanish (

S

). From a survey of

200

students, the following data were collected: -

80

students study French -

65

students study German -

70

students study Spanish -

30

students study both French and German -

25

students study both French and Spanish -

20

students study both German and Spanish -

10

students study all three languages

(a)

Determine the number of students who study at least one of the three languages. [3 marks]

(b)

Determine the probability that a randomly selected student from the survey studies exactly one language. [3 marks]

(c)

Given that a student studies French, determine the probability that they study exactly one of German or Spanish (but not both). [2 marks]

(d)

Determine the number of students who study none of the three languages. [1] (e) Determine the probability that a randomly selected student studies at least two languages, given that they study at least one language. [2 marks]

Solutions

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