CIE iGCSE Maths C8.2 Relative and expected frequencies Exam Style Practice Questions- Paper 1

Question

One of the 6 letters is taken at random.

(a) Write down the probability that the letter is S.

(b) The letter is replaced and again a letter is taken at random.

This is repeated 600 times.

How many times would you expect the letter to be S?

▶️ Answer/Explanation

Solution

(a) Ans: \(\frac{2}{6}\) or \(\frac{1}{3}\)

The word “S T A T E S” has 6 letters, with 2 being ‘S’.

Probability of selecting ‘S’ = \(\frac{\text{Number of ‘S’ letters}}{\text{Total letters}} = \frac{2}{6} = \frac{1}{3}\).

(b) Ans: 200

Expected frequency = Probability × Total trials.

\(\frac{1}{3} \times 600 = 200\).

Question

Ying spins a spinner 75 times.
The table shows her results.

(a) Write down the relative frequency of the spinner stopping on blue.

(b) Tony spins the same spinner 450 times.
Find the expected number of times the spinner stops on yellow.

▶️ Answer/Explanation

Solution

(a) Ans: \(\frac{24}{75}\) or equivalent

The relative frequency of blue is the number of times blue occurred (24) divided by the total spins (75).

Thus, \(\text{Relative Frequency} = \frac{24}{75}\), which simplifies to \(\frac{8}{25}\).

(b) Ans: 84

From the table, the experimental probability of yellow is \(\frac{14}{75}\).

For 450 spins, the expected number of yellows is \(450 \times \frac{14}{75} = 84\).

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