According to the Law of Large Numbers, what is the relationship between experimental and theoretical probability, or is there one at all? If you repeat an experiment many many times, you would expect: Select one or more: a. experimental probability to get further away form the theoretical probability. b. there to be no distinct pattern in the relationship between the experimental probability and theoretical probability. c. the experimental probability to never change. d. experimental probability to get closer and closer to the theoretical probability. Check

According to the **Law of Large Numbers**, as the number of trials in an experiment increases, the **experimental probability** (also known as the relative frequency) will tend to get closer to the **theoretical probability** (the probability predicted by theory). Let's evaluate each option: a. **Experimental probability to get further away from the theoretical probability.** - **Incorrect.** The Law of Large Numbers states the opposite; the experimental probability converges toward the theoretical probability. b. **There to be no distinct pattern in the relationship between the experimental probability and theoretical probability.** - **Incorrect.** There is a distinct pattern of convergence as more trials are conducted. c. **The experimental probability to never change.** - **Incorrect.** The experimental probability can fluctuate with each trial, especially in the short term, but it stabilizes as more trials are conducted. d. **Experimental probability to get closer and closer to the theoretical probability.** - **Correct.** This is a direct consequence of the Law of Large Numbers. **Correct Answer:** **d. experimental probability to get closer and closer to the theoretical probability.**