Sandy used a virtual coin toss app to show the results of flipping a coin 80 times, 800 times, and 3,000 times. Explain what most likely happened in Sandy's experiment.

Question

Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 80 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 800 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 3,000 flips.

Answer 1

To determine the most likely outcome in Sandy's experiment, we need to understand the relationship between experimental and theoretical probability.

Experimental probability is obtained through actual experimentation and counting the occurrence of an event. Theoretical probability, on the other hand, is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

In this case, the event is flipping a coin, which has two possible outcomes - heads or tails. Therefore, the theoretical probability of getting heads or tails is 1/2 or 0.5.

Now, let's consider Sandy's experiments:

1. If Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments, it means that she had a 50% chance of getting heads or tails in each experiment. However, since she used a virtual coin toss app, the outcome was determined by an algorithm specific to the app, and thus, it is unlikely that she obtained the exact theoretical probability with each experiment.

2. If Sandy's experimental probability was closest to the theoretical probability in the experiment with 80 flips, it implies that the more flips she conducted, the closer her experimental probability became to the theoretical probability. This aligns with the Law of Large Numbers, which states that as the number of trials increases, the experimental probability tends to converge to the theoretical probability.

3. Similar to point 2, if Sandy's experimental probability was closest to the theoretical probability in the experiment with 800 or 3,000 flips, it further emphasizes the Law of Large Numbers, suggesting that the more trials she conducted, the closer her experimental probability became to the theoretical probability.

Therefore, the most likely outcome in Sandy's experiment is that her experimental probability was closest to the theoretical probability in the experiment with 800 or 3,000 flips, as these larger sample sizes would provide more accurate estimates of the true probability.