For condition 2, a random sample of students is selected. The picture is bell-shaped with a mean of 0.12 and standard deviation of 0.023. Yes, it would be very unlikely.
People think they are likely to be better than average on most things.
Now the picture is even more compact. Another way to see this is to compute the standardized score for a proportion of 0.50. No, it is not in danger. So it is not impossible, but quite unlikely. The Rule for Sample Means says that the standard deviation of the frequency curve for the samples will be the population standard deviation divided by the square root of the sample size.