K \( 10(5.1,5.2) \) Choose the correct answer below. A. As the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to 0 . Casinos use the Law of Large Numbers to determ how many players gamble in certain games. B. As the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets gambling casinos? make a profit in the long run because they have a small statistical advantage in each game. C. This applies to casinos because they are able to 1 Large number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the the probability of the outcome. Casinos use the Law players gamble in certain games. D. As the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the probability of the outcome. This applies to casino: because they are able to make a profit in the long run because they have a small statistical advantage in each game.

**Step 1:** Identify the statement regarding the Law of Large Numbers. The Law of Large Numbers says that as the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the probability of that outcome. **Step 2:** Analyze the options: - **Option A:** It incorrectly states that the observed proportion gets closer to \(0\) rather than the probability of the outcome. Additionally, the connection to casinos is misstated. - **Option B:** While it hints at casinos making a profit, it does not correctly state the Law of Large Numbers. - **Option C:** Although it begins correctly by stating that the proportion converges to the outcome's probability, the explanation regarding casinos is incomplete. - **Option D:** It correctly explains that as the number of repetitions increases, the observed proportion gets closer to the outcome’s probability. It then accurately relates this to casinos, stating that they can make a profit in the long run due to a small statistical advantage in each game. **Step 3:** Since Option D is the only one that fully and correctly describes both the Law of Large Numbers and its application in casino games, the correct answer is: **D.** As the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the probability of the outcome. This applies to casino: because they are able to make a profit in the long run because they have a small statistical advantage in each game.