1. **Problem (a):** Nila claims she has a 50:50 chance of having one of her numbers drawn first in a lotto where 4 numbers are drawn from 1 to 24. 2. **Understanding the problem:** The lotto draw picks 4 numbers out of 24 without replacement. Nila chooses 4 numbers. The question is about the probability that the first number drawn is one of Nila's chosen numbers. 3. **Formula and reasoning:** The probability that the first number drawn is one of Nila's 4 chosen numbers is $ \frac{4}{24} = \frac{1}{6} $, not 50:50 (which means $ \frac{1}{2} $). 4. **Conclusion:** Nila's statement is incorrect because the chance is $ \frac{1}{6} $, not $ \frac{1}{2} $. --- 5. **Problem (b)(i):** The relative frequency of tails is 0.3. Find the relative frequency of heads. 6. **Formula:** Relative frequencies sum to 1, so relative frequency of heads = $1 - 0.3 = 0.7$. --- 7. **Problem (b)(ii):** The coin landed on tails 150 times. Find total tosses. 8. **Formula:** Relative frequency = $ \frac{\text{number of tails}}{\text{total tosses}} \Rightarrow 0.3 = \frac{150}{\text{total tosses}} $. 9. **Solve for total tosses:** $$ \text{total tosses} = \frac{150}{0.3} = 500 $$ --- 10. **Problem (b)(iii):** Is the coin biased? 11. **Reasoning:** A fair coin has equal probability 0.5 for heads and tails. Here, tails frequency is 0.3, heads 0.7, which is not equal. 12. **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.