To determine which student is most likely to find that the actual number of heads-up outcomes most closely matches the predicted number of heads-up outcomes, we need to consider the concept of the Law of Large Numbers.
The Law of Large Numbers states that as the number of trials increases, the experimental probability (the observed frequency of heads) will get closer to the theoretical probability (which, for a fair coin, is 50%). Hence, the more times a student flips the coin, the more accurate their results are likely to be in reflecting the true probability of landing heads up.
Let's look at the number of flips each student performs:
- Ana: 50 flips
- Brady: 10 flips
- Collin: 80 flips
- Deshawn: 20 flips
Since Collin has the highest number of flips with 80 flips, he is the most likely to have his results closely match the expected probability of 50% heads. This is due to the larger sample size reducing the relative effect of random variation.
Therefore, Collin is most likely to find the actual number of heads-up landings closest to the predicted number of heads-up landings.
