Question

juanita rolls a number cube x times. for which value of x are the experimental probability and the theoretical probability most likely to be equivalent?
1
6
600
1,000

Explanation:

Step1: Recall Probability Law

The Law of Large Numbers states that as the number of trials (rolls, in this case) increases, the experimental probability approaches the theoretical probability.

Step2: Analyze Options

• For \( x = 1 \): Only 1 roll, experimental probability will be very far from theoretical (since it's just one outcome).
• For \( x = 6 \): 6 rolls, still a small number of trials, experimental probability may not be close to theoretical.
• For \( x = 600 \): 600 rolls, more trials than 1 or 6, but less than 1000.
• For \( x = 1000 \): 1000 rolls, the largest number of trials among the options. By the Law of Large Numbers, the more trials, the closer experimental probability is to theoretical probability. So with 1000 rolls, experimental and theoretical probabilities are most likely to be equivalent.

Answer:

1,000 (the option with \( x = 1000 \))