Question

ma conducted an experiment by flipping a fair coin 200 times. the coin landed heads up 110 times. which statement about the coin landing heads up in ma’s experiment is correct?
options (paraphrased from ocr):

• the experimental probability of the coin landing heads up is \\(\frac{11}{20}\\) and the theoretical probability of the coin landing heads up is \\(\frac{1}{2}\\).
• the experimental probability of the coin landing heads up is \\(\frac{1}{2}\\) and the theoretical probability of the coin landing heads up is \\(\frac{11}{20}\\).
• the experimental probability of the coin landing heads up is \\(\frac{11}{20}\\) and the theoretical probability of the coin landing heads up is \\(\frac{11}{20}\\).
• the experimental probability of the coin landing heads up is \\(\frac{1}{2}\\) and the theoretical probability of the coin landing heads up is \\(\frac{1}{2}\\).

Explanation:

Step1: Calculate Experimental Probability

Experimental probability is the number of successful trials divided by the total number of trials. Here, successful trials (heads) = 110, total trials = 200. So experimental probability = $\frac{110}{200}=\frac{11}{20}$.

Step2: Determine Theoretical Probability

A fair coin has 2 sides (heads and tails), so the theoretical probability of heads is $\frac{1}{2}$ (since there's 1 favorable outcome out of 2 possible).

Answer:

The statement "The experimental probability of the coin landing heads up is $\frac{11}{20}$ and the theoretical probability of the coin landing heads up is $\frac{1}{2}$" is correct.