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Probability · Paper 1 — Free Maths AI SL Practice Questions

What this topic covers

This is the topic examiners lean on hardest, because it's the one place they can test whether you actually understand what a number means, not just whether you can press the right calculator button. A GDC will hand you $r$ , a $p$ -value, or a confidence interval in seconds — the marks live in knowing which tool to reach for, reading the question for the tail direction, and finishing with a sentence back in context. Four threads run through it: describing data you already have, inferring about a population you don't, modelling chance for single events, and modelling chance across a whole range of outcomes. They constantly borrow from each other, so treat this as one connected chapter, not four separate ones.

Read the full Statistics and Probability lesson notes →

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

A bag contains

12

red marbles and

8

blue marbles. Two marbles are selected at random from the bag without replacement.

(a)

State the probability that the first marble selected is red. [1 mark]

(b)

Calculate the probability that both marbles selected are red. [2 marks]

(c)

A game is played where a player wins USD 5 for each red marble drawn and loses USD 3 for each blue marble drawn. Determine the expected monetary outcome for a player who draws two marbles without replacement. [2 marks]

Solutions

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

A fair six-sided die is rolled twice. The faces are numbered $1, 2, 3, 4, 5, 6$.

(a)

State the probability of rolling a multiple of

3

on a single roll. [1 mark]

(b)

Find the probability that neither roll shows a multiple of

3

. [2 marks]

(c)

Given that the sum of the two rolls is

7

, find the probability that neither roll showed a multiple of

3

. [2 marks]

Solutions

3MasterySAQ-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 chosen student plays football but not basketball is

0.35

. [2 marks]

(b)

Hence find the probability that a randomly chosen student plays neither sport. [3 marks]

Solutions

4ChallengeSAQ-LBasic probability concepts and rules8 marksPaper 1~12 min

In a medical screening test for a certain disease, the following probabilities are known: - The probability that a randomly selected person has the disease is

0.02

- If a person has the disease, the probability that the test is positive is

0.95

- If a person does not have the disease, the probability that the test is positive is

0.04

(a)

Calculate the probability that a randomly selected person tests positive. [3 marks]

(b)

Given that a person tests positive, calculate the probability that they actually have the disease. [3 marks]

(c)

Evaluate whether this test is a reliable standalone screening tool. Justify your answer using the result from part (b) and the overall disease prevalence. [2 marks]

Solutions

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