Compare the empirical probabilities to the probability obtained using the classical method, and explain what they show. Choose the correct answer below. A. The empirical probabilities are all equally far away from the classical probability. This is an outcome expected according to the Law of Large Numbers. B. The empirical probability is closest to the classical probability for the two sets of 100 trials and gets farther away for the 500 trials. This is an outcome expected according to the Law of Large Numbers. C. All the empirical probabilities are equal to the classical probability. This is an outcome expected according to the Law of Large Numbers. D. The empirical probabilities approach the classical probability as the sample size increases. This is an outcome expected according to the Law of Large Numbers.

The empirical probabilities approach the classical probability as the sample size increases. This is an outcome expected according to the Law of Large Numbers.

Step-by-step explanation:

Empirical probabilities are probabilities obtained from actual results of experimental procedures. The probability of an event is the number of successes for that evemy divided by the total number of trials.

For example, if a coin is tossed 10 times, and a head is obtained 6 times, the probability of obtaining a head for the coin is (6/10) = 0.6.

This is empirical probability.

Classical probability, also referred to as theoretical probability is used to describe the random event has a given set of possible outcomes and that each possible outcome has an equal chance of happening/occurring.

For the example used under empirical probability, in 10 trials, theoretical/classical probability explains that a head will show up 5 times. The only two outcomes for a coin toss are a head and a tail. So, theoretical Probabilty shows that of a head is (1/2) = 0.5

The law of large numbers uses theoretical probability to approximate the actual successes that would be obtained from a statistical experiment with a particular number of trials, that is, uses classical probability to approximate empirical probabilty.

The actual statement of the law explains that for large number trials of an event, the actual number of successes approximates that predicted by the theoretical probability of that event.

So, the empirical probabilities approach the classical probability as the sample size increases. This is an outcome expected according to the Law of Large Numbers.

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