Which statement about probability is true?

Which statement about probability is true?

• A. The probability of an event that is absolutely certain is 0.
• B. The accuracy of theoretical probabilities depends on the size and representative nature of the samples being studied.
• C. Risk management professionals use theoretical probabilities because they are generally available for and applicable to claim analysis.
• D. Probabilities associated with events such as coin tosses can be developed from theoretical considerations and are unchanging.

Answer: (D)

Probabilities derived from a theoretical model are fixed under the model’s assumptions. For a coin toss, the probability of heads is 1/2, and that value doesn’t change from trial to trial as long as the coin is fair and the conditions stay the same. These theoretical probabilities come from reasoning about symmetry or counting outcomes, not from past outcomes, so they remain constant under the modeled scenario. This is why that statement is true: probabilities for simple random experiments like coin tosses can be developed from theoretical considerations and are unchanging when the underlying assumptions hold. Why the others don’t fit: a certain event has probability 1, not 0; empirical accuracy relates to observed frequencies and depends on sample size and representativeness rather than the theoretical probability itself; and although theoretical probabilities can be useful in risk analysis, they aren’t always readily available or applicable in every claim-analysis context.

Probabilities derived from a theoretical model are fixed under the model’s assumptions. For a coin toss, the probability of heads is 1/2, and that value doesn’t change from trial to trial as long as the coin is fair and the conditions stay the same. These theoretical probabilities come from reasoning about symmetry or counting outcomes, not from past outcomes, so they remain constant under the modeled scenario.

This is why that statement is true: probabilities for simple random experiments like coin tosses can be developed from theoretical considerations and are unchanging when the underlying assumptions hold.

Why the others don’t fit: a certain event has probability 1, not 0; empirical accuracy relates to observed frequencies and depends on sample size and representativeness rather than the theoretical probability itself; and although theoretical probabilities can be useful in risk analysis, they aren’t always readily available or applicable in every claim-analysis context.