5. Betina says that the product being less than 10 and the product being more than 10 are complementary events. Davika disagrees. Who is correct? Explain your reasoning. DQvikQ is coriect becquse product \( <10 \) and produst \( >10 \) do not cover cell possible

Davika is **correct** in this scenario. Here's why: ### Understanding Complementary Events **Complementary events** are two outcomes that satisfy the following conditions: 1. **Mutually Exclusive**: Both events cannot occur simultaneously. 2. **Exhaustive**: Together, they cover all possible outcomes in the sample space. When two events meet these criteria, the probability of one happening is equal to 1 minus the probability of the other happening. ### Applying to the Problem - **Betina's Claim**: - **Event A**: The product is **less than 10**. - **Event B**: The product is **more than 10**. Betina claims that Event A and Event B are complementary. - **Davika's Counterpoint**: - **Event C**: The product is **exactly 10**. ### Analysis 1. **Mutually Exclusive**: - **Event A** and **Event B** are mutually exclusive because if the product is less than 10, it cannot simultaneously be more than 10, and vice versa. 2. **Exhaustive**: - **Event A** and **Event B** do **not** cover all possible outcomes because there's a third possibility where the product is **exactly 10**. - This means that there's an outcome where neither Event A nor Event B occurs. ### Conclusion Since **Event A** and **Event B** do not account for the scenario where the product is exactly 10, they **do not** encompass all possible outcomes. Therefore, they **do not** satisfy the conditions to be complementary events. **Davika is correct** because Betina's claim overlooks the case where the product equals exactly 10, making the events not complementary.