CIE iGCSE Maths E8.2 Relative and expected frequencies Exam Style Practice Questions- Paper 2

Question

The table shows the relative frequency of the games won by a football team.

Result of game	won	lost	drawn
Relative frequency	0.1

The number of games lost is twice the number of games drawn.

Complete the table.

▶️ Answer/Explanation

Solution

Ans: lost 0.6, drawn 0.3

Total probability = 1 → remaining = 0.9.

Let drawn = x → lost = 2x → x + 2x = 0.9 → x = 0.3.

Thus drawn = 0.3, lost = 0.6.

Question

A company surveys 40 of its employees.

In the survey, 3 employees say they walk to work.

The company has a total of 1240 employees.

Find the expected number of employees in the company who walk to work.

▶️ Answer/Explanation

Solution

Answer: 93 employees

Method 1: Using Proportion

1. Find the survey proportion who walk:

\(\frac{3}{40} = 0.075\) (or 7.5%)

2. Apply to total employees:

\(0.075 \times 1240 = 93\)

Method 2: Cross-Multiplication

\(\frac{3}{40} = \frac{x}{1240}\)

\(3 \times 1240 = 40 \times x\)

\(3720 = 40x\)

\(x = \frac{3720}{40} = 93\)

Verification:

• 93/1240 ≈ 0.075 (matches survey proportion)

• Both methods give consistent results

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