Final answer:
In the class survey with coin flipping, 18 'yes' and 12 'no' answers were recorded. If a fair coin is flipped, the theoretical probability of heads is 0.5. By subtracting the expected 'yes' responses due to heads from the actual 'yes' responses, it's estimated that approximately 3 students might have used a fake ID.
Step-by-step explanation:
In the class survey scenario where 30 students flip a coin and answer a question based on the result—saying 'yes' for heads and giving an honest answer for tails to the question of having used a fake ID—the results are 18 'yes' and 12 'no' responses. To analyze these results, we need to consider the probability of flipping heads, which is 0.5 (or 50%), as per theoretical probability. Since heads require a 'yes' response, some of these 'yes' answers may be honest, while others are dictated by the coin flip.
The challenge is to estimate the actual number of students who have used a fake ID, knowing that half the time, students should get heads on a fair coin toss and say 'yes' regardless of their personal history with fake IDs. Considering theoretical outcomes, we'd expect approximately half of the 30 students, so about 15, to flip heads and automatically say 'yes.' The 18 'yes' answers we see could imply that some students (about 3) are honestly admitting to having used a fake ID. However, since there's variance in actual outcomes, and the probability doesn't guarantee exactly half the outcomes to be heads in a small sample, we're dealing with uncertainty. The actual count could be slightly different due to the randomness of each coin toss.
To estimate the number of students who have honestly answered 'yes,' we would subtract the expected number of 'yes' from the coin toss (around 15) from the actual number of 'yes' responses (18), which gives us an estimate of 3 students who might have used a fake ID. However, this is just an estimate and subject to the randomness in the sample of 30 flips.