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.

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)

Answer 1

Part A:

The theoretical probability of a fair coin landing on heads is 1/2 or 0.5.

Part B:

Here are the results of flipping a coin 20 times and recording the frequency of each outcome:
- Heads: 10
- Tails: 10

Part C:

The experimental probability of landing on heads is calculated by taking the number of successful outcomes (in this case, landing on heads) divided by the total number of trials. In this case, the experimental probability of landing on heads is 10/20 = 0.5.

Part D:

The theoretical and experimental probabilities are the same in this case because the coin is fair and unbiased. The probability of landing on heads is expected to be 0.5 according to theory, and in this experiment, where the coin was flipped 20 times, the experimental probability of 0.5 matches the theoretical probability of 0.5. This suggests that the coin used was fair and that the results are consistent with what would be expected based on theoretical probability.