Mark spins a penny 100 times and it lands head side up 41 times.
A.Explain why Mark's experimental probability may be different from the theoretical probability of spinning a coin.
B.Explain what would happen to Mark's experimental probability if he continued to spin the penny 1,000 times?
(10 points)
A. Mark's experimental probability may be different from the theoretical probability of spinning a coin due to natural variability and chance. Theoretical probability is based on the assumption of an ideal situation where all outcomes are equally likely, but in reality, there are many factors that can affect the outcome of each spin, such as how the coin is spun, the surface it lands on, and any bias in the coin itself. In this case, the result of landing head side up 41 times out of 100 spins could just be a random variation from the expected 50% probability for a fair coin.
B. If Mark continued to spin the penny 1,000 times, the experimental probability of landing head side up may approach the theoretical probability of 50% more closely. This is because as the number of trials increases, the result is likely to converage towards the true probability. By increasing the number of spins, any random variations or biases in the coin are more likely to be balanced out and the actual experimental probability will be more reflective of the expected theoretical probability.