Law of Large Numbers

What is the Law of Large Numbers?

• The Law of Large Numbers states that as a probabilistic process is repeated a large number of times, the experimental probability of its possible outcomes will get closer to their respective theoretical probabilities.

• The Law of Large Numbers states that the outcomes of a probabilistic process are always predictable after a few trials.

• The Law of Large Numbers indicates that all outcomes of a probabilistic process will occur with equal frequency.

• The Law of Large Numbers suggests that increasing the number of trials will lead to a decrease in the variability of outcomes.

In a 'Guess the Number of Jelly Beans in the Jar' contest, how many guesses maximize your chances of winning?

• 100 guesses

• 500 guesses

• 1,000 guesses

• 2,000 guesses

What happens to experimental probability as the number of trials increases?

• The experimental probability becomes random and unpredictable.

• The experimental probability will come closer to the theoretical probability.

• The experimental probability will always remain the same regardless of trials.

• The experimental probability will decrease with more trials.

What is a fair coin?

• A coin that has an equal chance of landing on heads or tails, with a probability of 0.5 for each side.

• A coin that is biased towards heads, with a probability of 0.7 for heads and 0.3 for tails.

• A coin that is weighted to always land on tails.

• A coin that has a 60% chance of landing on heads and a 40% chance of landing on tails.

What is the difference between theoretical probability and experimental probability?

• Theoretical probability is based on expected outcomes, while experimental probability is based on actual results from trials.

• Theoretical probability is calculated using past data, while experimental probability is purely theoretical.

• Theoretical probability is always higher than experimental probability.

• Theoretical probability is based on actual results, while experimental probability is based on expected outcomes.

If you toss a fair coin 10,000 times and it lands on heads 4,989 times, is the theoretical probability and experimental probability getting further away from each other?

• True. They will get further away as the number of trials increases.

• False. They will get closer as the number of trials increases.

• True. The experimental probability will always differ from the theoretical probability.

• False. The experimental probability will never converge with the theoretical probability.

What is the role of randomness in the Law of Large Numbers?

• Randomness ensures that over a large number of trials, the outcomes will average out to the expected theoretical probabilities.

• Randomness introduces variability that prevents any predictable outcomes from occurring.

• Randomness is irrelevant as the Law of Large Numbers only applies to deterministic processes.

• Randomness guarantees that all outcomes will be equally likely in every trial.

What is the significance of increasing the number of trials in an experiment?

• It reduces the time required for the experiment.

• It ensures that the experimental probability converges to the theoretical probability.

• It eliminates all sources of error in the experiment.

• It guarantees a successful outcome every time.

What is the theoretical probability of getting heads when tossing a fair coin?

• 0.25 or 25%

• 0.5 or 50%

• 0.75 or 75%

• 1 or 100%

What is the experimental probability of an event?

• The experimental probability is the ratio of the number of times an event occurs to the total number of trials conducted.

• The experimental probability is the likelihood of an event based on theoretical calculations.

• The experimental probability is the percentage of successful outcomes in a single trial.

• The experimental probability is determined by the number of favorable outcomes divided by the total number of possible outcomes.