In Exercises 7-12, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.
11. The probability of rolling 2 six-sided dice and getting a sum of 9 is 1/9.

검증된 단계별 안내

Step 1: Understand the three types of probability: Classical probability is based on theoretical reasoning and assumes equally likely outcomes. Empirical probability is based on observed data or experiments. Subjective probability is based on personal judgment or opinion.

Step 2: Analyze the given statement. The problem states that the probability of rolling two six-sided dice and getting a sum of 9 is 1/9. This probability is derived from theoretical reasoning about the possible outcomes of rolling two dice.

Step 3: Recall that classical probability is calculated using the formula:

\frac{favorable outcomes}{total outcomes}

. In this case, the favorable outcomes are the combinations of dice rolls that result in a sum of 9, and the total outcomes are all possible combinations of rolling two dice.

Step 4: Determine whether the probability is based on theoretical reasoning or observed data. Since the probability is calculated using the theoretical number of favorable outcomes divided by the total number of outcomes, it is an example of classical probability.

Step 5: Conclude that the statement is an example of classical probability because it is derived from theoretical calculations rather than experimental data or personal judgment.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Classical Probability

Classical probability is based on the assumption that all outcomes in a sample space are equally likely. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, when rolling two six-sided dice, the total number of outcomes is 36, and the number of ways to achieve a sum of 9 can be counted, leading to a probability calculation.

Empirical Probability

Empirical probability is determined through experimentation or observation rather than theoretical calculations. It is calculated by taking the ratio of the number of times an event occurs to the total number of trials conducted. This type of probability is useful when theoretical probabilities are difficult to ascertain or when real-world data is available.

Subjective Probability

Subjective probability is based on personal judgment, intuition, or experience rather than on exact calculations or empirical data. It reflects an individual's belief about the likelihood of an event occurring. This type of probability can vary significantly between individuals and is often used in situations where statistical data is limited or unavailable.

In Exercises 7-12, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.11. The probability of rolling 2 six-sided dice and getting a sum of 9 is 1/9.