1. **Problem statement:** Mia writes down five whole numbers and picks one at random. Outcome E is picking an even number, and outcome O is picking an odd number. We need to determine for two statements whether they must be true, could be true, or must be false. 2. **Understanding the problem:** Mia has 5 whole numbers. Each number is either even or odd. Outcome E is the event of picking an even number, and outcome O is picking an odd number. 3. **Statement 1: "Outcome E is more likely to happen than outcome O"** - This means the number of even numbers is greater than the number of odd numbers. - Since Mia chooses 5 numbers, possible distributions of even and odd numbers are: - 5 even, 0 odd - 4 even, 1 odd - 3 even, 2 odd - 2 even, 3 odd - 1 even, 4 odd - 0 even, 5 odd - Outcome E is more likely than O only if even numbers > odd numbers, i.e., 3, 4, or 5 even numbers. - But Mia could have any combination, so this statement: - **Could be true** (if more evens) - **Could be false** (if more odds) - It **does not have to be true** always 4. **Statement 2: "Outcome E and outcome O can happen at the same time"** - This means it is possible to pick a number that is both even and odd simultaneously. - Since a number cannot be both even and odd at the same time, this is impossible. - However, the question might mean if both outcomes can occur in the sample space (i.e., the set of numbers contains both even and odd numbers). - If Mia's 5 numbers include at least one even and one odd number, then both outcomes can happen (depending on which number is picked). - So: - It **could be true** if the list contains both even and odd numbers. - It **must be false** if all numbers are only even or only odd. - Therefore, the statement "Outcome E and outcome O can happen at the same time" is: - **Could be true** **Final answers:** - Outcome E is more likely than outcome O: Could be true [✓] - Outcome E and outcome O can happen at the same time: Could be true [✓]