Which statement regarding probability is correct?

Which statement regarding probability is correct?

• A. Probabilities associated with events such as coin tosses can be developed from theoretical considerations and are unchanging.
• B. The accuracy of theoretical probabilities depends on the size and representative nature of the samples being studied.
• C. Probabilities associated with events such as coin tosses are always changing and not necessarily predictable.
• D. The probability of an event that is absolutely certain is 0.

Answer: (A)

Probabilities derived from theory are fixed within the assumed model. For a fair coin, theory says the chance of heads is 0.5, and this probability does not change from toss to toss even though the outcomes are random. These probabilities come from the underlying assumptions and remain constant as long as those assumptions (like fairness and independence) hold. Observed results from finite samples can deviate from the theoretical probability, and larger, representative samples help these empirical frequencies better reflect the theory. The idea that probabilities are always changing or not predictable isn’t consistent with having a stable probabilistic model. And an event that is absolutely certain has probability 1, not 0.

Probabilities derived from theory are fixed within the assumed model. For a fair coin, theory says the chance of heads is 0.5, and this probability does not change from toss to toss even though the outcomes are random. These probabilities come from the underlying assumptions and remain constant as long as those assumptions (like fairness and independence) hold. Observed results from finite samples can deviate from the theoretical probability, and larger, representative samples help these empirical frequencies better reflect the theory. The idea that probabilities are always changing or not predictable isn’t consistent with having a stable probabilistic model. And an event that is absolutely certain has probability 1, not 0.