1. **Problem statement:** (a) Nila claims she has a 50:50 chance of having one of her 4 chosen numbers drawn first from numbers 1 to 24. 2. **Understanding the problem:** Nila picks 4 numbers out of 24. The chance of the first number drawn being one of her 4 numbers is the number of favorable outcomes over total outcomes. 3. **Formula:** Probability = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} 4. **Calculate the probability:** $$\text{Probability} = \frac{4}{24} = \frac{1}{6} \approx 0.1667$$ 5. **Interpretation:** Nila's chance is about 16.67%, not 50%. So, her statement is incorrect. 6. **Reason:** The chance of the first number drawn being one of Nila's 4 numbers is \frac{4}{24}, which is much less than 50%. Therefore, the statement "I have a 50:50 chance" is false. --- (b)(i) The relative frequency of tails is 0.3. 7. **Calculate relative frequency of heads:** Since total probability must sum to 1, $$\text{Relative frequency of heads} = 1 - 0.3 = 0.7$$ (b)(ii) The coin landed on tails 150 times. 8. **Calculate total tosses:** Let total tosses be $T$. $$0.3 \times T = 150$$ $$T = \frac{150}{0.3} = 500$$ (b)(iii) Is the coin biased? 9. **Interpretation:** A fair coin has equal chances for heads and tails (0.5 each). Here, tails is 0.3 and heads is 0.7, which is not equal. 10. **Conclusion:** The coin is biased because the relative frequencies are not equal. --- Final answers: (a) Nila’s statement is incorrect. (b)(i) Relative frequency of heads is 0.7. (b)(ii) Total tosses = 500. (b)(iii) The coin is biased.