Question

A coin is flipped at the start of every game to determine if Team A (heads) or Team B (tails) will get the ball first.

Part A: Find the theoretical probability of a fair coin landing on heads. (2 points)


Part B: Flip a coin 20 times and record the frequency of each outcome. (4 points)


Part C: Determine the experimental probability of landing on heads. (4 points)


Part D: Compare the theoretical and experimental probabilities. Explain your answer. (2 points)


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Answer 1

Explanation:

Part A: The theoretical probability of a fair coin landing on heads is 0.5 or 50%. This is because there are two possible outcomes for a coin flip: heads or tails, and assuming the coin is fair, each outcome has an equal chance of occurring.

Part B: The frequency of each outcome after flipping a coin 20 times may vary due to chance, but it is expected to be close to the theoretical probability of 0.5 for heads and 0.5 for tails.

Part C: The experimental probability of landing on heads can be calculated by dividing the frequency of landing on heads by the total number of coin flips. In this example, the experimental probability of landing on heads is:

Experimental probability of landing on heads = 11/20 = 0.55 or 55%

Part D: The theoretical probability of landing on heads is 0.5 or 50%, while the experimental probability of landing on heads after flipping a coin 20 times is 0.55 or 55%. This difference between theoretical and experimental probabilities may be due to chance variation, as the experimental probability is based on a finite number of trials. However, with more trials, the experimental probability is expected to converge to the theoretical probability