Question

Question

Anita states that experimental and theoretical probabilities are always the same.

Is Anita's statement true? Why or why not?

Responses

Yes, experimental and theoretical probabilities are always the same.
Yes, experimental and theoretical probabilities are always the same.

No, experimental probabilities are often different from theoretical probabilities.
No, experimental probabilities are often different from theoretical probabilities.

No, experimental probabilities and theoretical probabilities are never the same.
No, experimental probabilities and theoretical probabilities are never the same.
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Answer 1

Anita's statement is not true. The correct response is:

No, experimental probabilities are often different from theoretical probabilities.

Explanation:

• Theoretical Probability is calculated based on the possible outcomes in a perfect scenario. For instance, the theoretical probability of rolling a 3 on a fair six-sided die is 1/6, as there are six possible outcomes, and each is equally likely.

• Experimental Probability is determined by conducting an actual experiment or trial and observing the outcomes. For example, if you roll a die 60 times and get a 3 on 10 of those rolls, the experimental probability of rolling a 3 is 10/60, which simplifies to 1/6.

Experimental probabilities can differ from theoretical probabilities due to various factors including the number of trials conducted, randomness, and potential biases in the experiment. As the number of trials increases, experimental probabilities tend to get closer to theoretical probabilities due to the Law of Large Numbers, but they are not guaranteed to be the same.