23.2 Relative frequency and expected outcomes — Practise

1. A player scores 21 times in 35 attempts. Find the relative frequency of scoring.

Answer: $\frac{21}{35}=\frac35$.

2. A spinner lands on green 42 times in 70 spins. Use this to estimate the probability of green.

Answer: $\frac{42}{70}=0.6$.

3. A fair coin lands on heads 7 times in 10 tosses. Is this result impossible for a fair coin?

Answer: No. A short sample can differ from the theoretical probability.

4. A fair die is rolled 300 times. Find the expected number of sixes.

Answer: $300\times\frac16=50$.

5. A spinner has probability $0.3$ of landing on red. Find the expected red results in 80 spins.

Answer: $0.3\times80=24$.

6. A team wins 16 of 40 games. Find the relative frequency as a percentage.

Answer: $40\%$.

7. An event has probability $\frac{2}{5}$. Find its expected frequency in 12 trials.

Answer: $\frac{24}{5}=4.8$; this is an expectation.

8. A sample suggests probability $0.62$. Estimate the number of successes in 200 trials.

Answer: $124$.

9. A shot misses 9 times in 30 attempts. Find the relative frequency of a miss.

Answer: $\frac3{10}$.

10. A fair die shows a 1 on 14 of 60 rolls. Compare the observed relative frequency with the theoretical probability.

Answer: $\frac{14}{60}>\frac16$ for this sample.